---
_id: '64816'
abstract:
- lang: eng
text: "We study a block mean-field Ising model with $N$ spins split into $s_N$ blocks,
with Curie-Weiss interaction within blocks and nearest-neighbor coupling between
blocks. While previous models deal with the block magnetization for a fixed number
of blocks, we study the the simultaneous limit $N\\to\\infty$ and $s_N\\to\\infty$.
The model interpolates between Curie-Weiss model for $s_N=1$, multi-species mean
field for fixed $s_N=s$, and the 1D Ising model for each spin in its own block
at $s_N=N$.\r\n Under mild growth conditions on $s_N$, we prove a law of large
numbers and a multivariate CLT with covariance given by the lattice Green's function.
For instance, the high temperature CLT essentially covers the optimal range up
to $s_N=o(N/(\\log N)^c)$ and the low temperature regime is new even for fixed
number of blocks $s > 2$. In addition to the standard competition between entropy
and energy, a new obstacle in the proofs is a curse of dimensionality as $s_N
\\to \\infty$."
author:
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Isabel
full_name: Lammers, Isabel
last_name: Lammers
- first_name: Matthias
full_name: Löwe, Matthias
last_name: Löwe
citation:
ama: Jalowy J, Lammers I, Löwe M. The infinite block spin Ising model. arXiv:260301994.
Published online 2026.
apa: Jalowy, J., Lammers, I., & Löwe, M. (2026). The infinite block spin Ising
model. In arXiv:2603.01994.
bibtex: '@article{Jalowy_Lammers_Löwe_2026, title={The infinite block spin Ising
model}, journal={arXiv:2603.01994}, author={Jalowy, Jonas and Lammers, Isabel
and Löwe, Matthias}, year={2026} }'
chicago: Jalowy, Jonas, Isabel Lammers, and Matthias Löwe. “The Infinite Block Spin
Ising Model.” ArXiv:2603.01994, 2026.
ieee: J. Jalowy, I. Lammers, and M. Löwe, “The infinite block spin Ising model,”
arXiv:2603.01994. 2026.
mla: Jalowy, Jonas, et al. “The Infinite Block Spin Ising Model.” ArXiv:2603.01994,
2026.
short: J. Jalowy, I. Lammers, M. Löwe, ArXiv:2603.01994 (2026).
date_created: 2026-03-03T08:49:16Z
date_updated: 2026-03-03T08:49:33Z
department:
- _id: '94'
external_id:
arxiv:
- '2603.01994'
language:
- iso: eng
publication: arXiv:2603.01994
status: public
title: The infinite block spin Ising model
type: preprint
user_id: '113768'
year: '2026'
...
---
_id: '59664'
abstract:
- lang: eng
text: "Given a sequence of polynomials $(P_n)_{n \\in \\mathbb{N}}$ with only\r\nnonpositive
zeros, the aim of this article is to present a user-friendly\r\napproach for determining
the limiting zero distribution of $P_n$ as\r\n$\\mathrm{deg}\\, P_n \\to \\infty$.
The method is based on establishing an\r\nequivalence between the existence of
a limiting empirical zero distribution\r\n$\\mu$ and the existence of an exponential
profile $g$ associated with the\r\ncoefficients of the polynomials $(P_n)_{n \\in
\\mathbb{N}}$. The exponential\r\nprofile $g$, which can be roughly described
by $[z^k]P_n(z) \\approx \\exp(n\r\ng(k/n))$, offers a direct route to computing
the Cauchy transform $G$ of $\\mu$:\r\nthe functions $t \\mapsto tG(t)$ and $\\alpha
\\mapsto \\exp(-g'(\\alpha))$ are\r\nmutual inverses. This relationship, in various
forms, has previously appeared\r\nin the literature, most notably in the paper
[Van Assche, Fano and Ortolani,\r\nSIAM J. Math. Anal., 1987].\r\n As a first
contribution, we present a self-contained probabilistic proof of\r\nthis equivalence
by representing the polynomials as generating functions of\r\nsums of independent
Bernoulli random variables. This probabilistic framework\r\nnaturally lends itself
to tools from large deviation theory, such as the\r\nexponential change of measure.
The resulting theorems generalize and unify a\r\nrange of previously known results,
which were traditionally established through\r\nanalytic or combinatorial methods.\r\n
\ Secondly, using the profile-based approach, we investigate how the\r\nexponential
profile and the limiting zero distribution behave under certain\r\noperations
on polynomials, including finite free convolutions, Hadamard\r\nproducts, and
repeated differentiation. In particular, our approach yields new\r\nproofs of
the convergence results `$\\boxplus_n \\to \\boxplus$' and `$\\boxtimes_n\r\n\\to
\\boxtimes$', extending them to cases where the distributions are not\r\nnecessarily
compactly supported."
author:
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Zakhar
full_name: Kabluchko, Zakhar
last_name: Kabluchko
- first_name: Alexander
full_name: Marynych, Alexander
last_name: Marynych
citation:
ama: 'Jalowy J, Kabluchko Z, Marynych A. Zeros and exponential profiles of polynomials
I: Limit distributions, finite free convolutions and repeated differentiation.
arXiv:250411593. Published online 2025.'
apa: 'Jalowy, J., Kabluchko, Z., & Marynych, A. (2025). Zeros and exponential
profiles of polynomials I: Limit distributions, finite free convolutions and
repeated differentiation. In arXiv:2504.11593.'
bibtex: '@article{Jalowy_Kabluchko_Marynych_2025, title={Zeros and exponential profiles
of polynomials I: Limit distributions, finite free convolutions and repeated
differentiation}, journal={arXiv:2504.11593}, author={Jalowy, Jonas and Kabluchko,
Zakhar and Marynych, Alexander}, year={2025} }'
chicago: 'Jalowy, Jonas, Zakhar Kabluchko, and Alexander Marynych. “Zeros and Exponential
Profiles of Polynomials I: Limit Distributions, Finite Free Convolutions and
Repeated Differentiation.” ArXiv:2504.11593, 2025.'
ieee: 'J. Jalowy, Z. Kabluchko, and A. Marynych, “Zeros and exponential profiles
of polynomials I: Limit distributions, finite free convolutions and repeated
differentiation,” arXiv:2504.11593. 2025.'
mla: 'Jalowy, Jonas, et al. “Zeros and Exponential Profiles of Polynomials I: Limit
Distributions, Finite Free Convolutions and Repeated Differentiation.” ArXiv:2504.11593,
2025.'
short: J. Jalowy, Z. Kabluchko, A. Marynych, ArXiv:2504.11593 (2025).
date_created: 2025-04-23T14:37:41Z
date_updated: 2025-04-23T14:38:04Z
department:
- _id: '94'
external_id:
arxiv:
- '2504.11593'
language:
- iso: eng
publication: arXiv:2504.11593
status: public
title: 'Zeros and exponential profiles of polynomials I: Limit distributions, finite
free convolutions and repeated differentiation'
type: preprint
user_id: '113768'
year: '2025'
...
---
_id: '59213'
abstract:
- lang: eng
text: "Abstract\r\n We compare a mean-field
Gibbs distribution on a finite state space on N spins
to that of an explicit simple mixture of product measures. This illustrates the
situation beyond the so-called increasing propagation of chaos
introduced by Ben Arous and Zeitouni [3], where marginal distributions of size
\r\n \r\n $$k=o(N)$$\r\n
\ \r\n
\ \r\n k\r\n =\r\n
\ o\r\n (\r\n
\ N\r\n )\r\n
\ \r\n \r\n \r\n
\ are compared to product measures."
article_number: '6'
author:
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Zakhar
full_name: Kabluchko, Zakhar
last_name: Kabluchko
- first_name: Matthias
full_name: Löwe, Matthias
last_name: Löwe
citation:
ama: Jalowy J, Kabluchko Z, Löwe M. Propagation of Chaos and Residual Dependence
in Gibbs Measures on Finite Sets. Mathematical Physics, Analysis and Geometry.
2025;28(1). doi:10.1007/s11040-025-09503-5
apa: Jalowy, J., Kabluchko, Z., & Löwe, M. (2025). Propagation of Chaos and
Residual Dependence in Gibbs Measures on Finite Sets. Mathematical Physics,
Analysis and Geometry, 28(1), Article 6. https://doi.org/10.1007/s11040-025-09503-5
bibtex: '@article{Jalowy_Kabluchko_Löwe_2025, title={Propagation of Chaos and Residual
Dependence in Gibbs Measures on Finite Sets}, volume={28}, DOI={10.1007/s11040-025-09503-5},
number={16}, journal={Mathematical Physics, Analysis and Geometry}, publisher={Springer
Science and Business Media LLC}, author={Jalowy, Jonas and Kabluchko, Zakhar and
Löwe, Matthias}, year={2025} }'
chicago: Jalowy, Jonas, Zakhar Kabluchko, and Matthias Löwe. “Propagation of Chaos
and Residual Dependence in Gibbs Measures on Finite Sets.” Mathematical Physics,
Analysis and Geometry 28, no. 1 (2025). https://doi.org/10.1007/s11040-025-09503-5.
ieee: 'J. Jalowy, Z. Kabluchko, and M. Löwe, “Propagation of Chaos and Residual
Dependence in Gibbs Measures on Finite Sets,” Mathematical Physics, Analysis
and Geometry, vol. 28, no. 1, Art. no. 6, 2025, doi: 10.1007/s11040-025-09503-5.'
mla: Jalowy, Jonas, et al. “Propagation of Chaos and Residual Dependence in Gibbs
Measures on Finite Sets.” Mathematical Physics, Analysis and Geometry,
vol. 28, no. 1, 6, Springer Science and Business Media LLC, 2025, doi:10.1007/s11040-025-09503-5.
short: J. Jalowy, Z. Kabluchko, M. Löwe, Mathematical Physics, Analysis and Geometry
28 (2025).
date_created: 2025-03-31T07:17:19Z
date_updated: 2025-04-23T14:39:12Z
doi: 10.1007/s11040-025-09503-5
intvolume: ' 28'
issue: '1'
language:
- iso: eng
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
issn:
- 1385-0172
- 1572-9656
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets
type: journal_article
user_id: '113768'
volume: 28
year: '2025'
...
---
_id: '59665'
article_number: '110974'
author:
- first_name: Matthias
full_name: Erbar, Matthias
last_name: Erbar
- first_name: Martin
full_name: Huesmann, Martin
last_name: Huesmann
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Bastian
full_name: Müller, Bastian
last_name: Müller
citation:
ama: 'Erbar M, Huesmann M, Jalowy J, Müller B. Optimal transport of stationary point
processes: Metric structure, gradient flow and convexity of the specific entropy.
Journal of Functional Analysis. 2025;289(4). doi:10.1016/j.jfa.2025.110974'
apa: 'Erbar, M., Huesmann, M., Jalowy, J., & Müller, B. (2025). Optimal transport
of stationary point processes: Metric structure, gradient flow and convexity of
the specific entropy. Journal of Functional Analysis, 289(4), Article
110974. https://doi.org/10.1016/j.jfa.2025.110974'
bibtex: '@article{Erbar_Huesmann_Jalowy_Müller_2025, title={Optimal transport of
stationary point processes: Metric structure, gradient flow and convexity of the
specific entropy}, volume={289}, DOI={10.1016/j.jfa.2025.110974},
number={4110974}, journal={Journal of Functional Analysis}, publisher={Elsevier
BV}, author={Erbar, Matthias and Huesmann, Martin and Jalowy, Jonas and Müller,
Bastian}, year={2025} }'
chicago: 'Erbar, Matthias, Martin Huesmann, Jonas Jalowy, and Bastian Müller. “Optimal
Transport of Stationary Point Processes: Metric Structure, Gradient Flow and Convexity
of the Specific Entropy.” Journal of Functional Analysis 289, no. 4 (2025).
https://doi.org/10.1016/j.jfa.2025.110974.'
ieee: 'M. Erbar, M. Huesmann, J. Jalowy, and B. Müller, “Optimal transport of stationary
point processes: Metric structure, gradient flow and convexity of the specific
entropy,” Journal of Functional Analysis, vol. 289, no. 4, Art. no. 110974,
2025, doi: 10.1016/j.jfa.2025.110974.'
mla: 'Erbar, Matthias, et al. “Optimal Transport of Stationary Point Processes:
Metric Structure, Gradient Flow and Convexity of the Specific Entropy.” Journal
of Functional Analysis, vol. 289, no. 4, 110974, Elsevier BV, 2025, doi:10.1016/j.jfa.2025.110974.'
short: M. Erbar, M. Huesmann, J. Jalowy, B. Müller, Journal of Functional Analysis
289 (2025).
date_created: 2025-04-23T14:39:50Z
date_updated: 2025-04-23T14:41:19Z
department:
- _id: '94'
doi: 10.1016/j.jfa.2025.110974
intvolume: ' 289'
issue: '4'
language:
- iso: eng
publication: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier BV
status: public
title: 'Optimal transport of stationary point processes: Metric structure, gradient
flow and convexity of the specific entropy'
type: journal_article
user_id: '113768'
volume: 289
year: '2025'
...
---
_id: '60293'
abstract:
- lang: eng
text: "In this work, we present a complete characterization of the covariance\r\nstructure
of number statistics in boxes for hyperuniform point processes. Under\r\na standard
integrability assumption, the covariance depends solely on the\r\noverlap of the
faces of the box. Beyond this assumption, a novel interpolating\r\ncovariance
structure emerges. This enables us to identify a limiting Gaussian\r\n'coarse-grained'
process, counting the number of points in large boxes as a\r\nfunction of the
box position. Depending on the integrability assumption, this\r\nprocess may be
continuous or discontinuous, e.g. in d=1 it is given by an\r\nincrement process
of a fractional Brownian motion."
author:
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Hanna
full_name: Stange, Hanna
last_name: Stange
citation:
ama: Jalowy J, Stange H. Box-Covariances of Hyperuniform Point Processes. arXiv:250613661.
Published online 2025.
apa: Jalowy, J., & Stange, H. (2025). Box-Covariances of Hyperuniform Point
Processes. In arXiv:2506.13661.
bibtex: '@article{Jalowy_Stange_2025, title={Box-Covariances of Hyperuniform Point
Processes}, journal={arXiv:2506.13661}, author={Jalowy, Jonas and Stange, Hanna},
year={2025} }'
chicago: Jalowy, Jonas, and Hanna Stange. “Box-Covariances of Hyperuniform Point
Processes.” ArXiv:2506.13661, 2025.
ieee: J. Jalowy and H. Stange, “Box-Covariances of Hyperuniform Point Processes,”
arXiv:2506.13661. 2025.
mla: Jalowy, Jonas, and Hanna Stange. “Box-Covariances of Hyperuniform Point Processes.”
ArXiv:2506.13661, 2025.
short: J. Jalowy, H. Stange, ArXiv:2506.13661 (2025).
date_created: 2025-06-22T08:02:28Z
date_updated: 2025-06-22T08:03:20Z
department:
- _id: '94'
external_id:
arxiv:
- '2506.13661'
language:
- iso: eng
publication: arXiv:2506.13661
status: public
title: Box-Covariances of Hyperuniform Point Processes
type: preprint
user_id: '113768'
year: '2025'
...
---
_id: '63394'
abstract:
- lang: eng
text: We study the statistics of the number of real eigenvalues in the elliptic
deformation of the real Ginibre ensemble. As the matrix dimension grows, the law
of large numbers and the central limit theorem for the number of real eigenvalues
are well understood, but the probabilities of rare events remain largely unexplored.
Large deviation type results have been obtained only in extreme cases, when either
a vanishingly small proportion of eigenvalues are real or almost all eigenvalues
are real. Here, in both the strong and weak asymmetry regimes, we derive the probabilities
of rare events in the moderate-to-large deviation regime, thereby providing a
natural connection between the previously known regime of Gaussian fluctuations
and the large deviation regime. Our results are new even for the classical real
Ginibre ensemble.
author:
- first_name: Sung-Soo
full_name: Byun, Sung-Soo
last_name: Byun
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Yong-Woo
full_name: Lee, Yong-Woo
last_name: Lee
- first_name: Grégory
full_name: Schehr, Grégory
last_name: Schehr
citation:
ama: Byun S-S, Jalowy J, Lee Y-W, Schehr G. Moderate-to-large deviation asymptotics
for real eigenvalues of the elliptic Ginibre matrices. arXiv:251109191.
Published online 2025.
apa: Byun, S.-S., Jalowy, J., Lee, Y.-W., & Schehr, G. (2025). Moderate-to-large
deviation asymptotics for real eigenvalues of the elliptic Ginibre matrices. In
arXiv:2511.09191.
bibtex: '@article{Byun_Jalowy_Lee_Schehr_2025, title={Moderate-to-large deviation
asymptotics for real eigenvalues of the elliptic Ginibre matrices}, journal={arXiv:2511.09191},
author={Byun, Sung-Soo and Jalowy, Jonas and Lee, Yong-Woo and Schehr, Grégory},
year={2025} }'
chicago: Byun, Sung-Soo, Jonas Jalowy, Yong-Woo Lee, and Grégory Schehr. “Moderate-to-Large
Deviation Asymptotics for Real Eigenvalues of the Elliptic Ginibre Matrices.”
ArXiv:2511.09191, 2025.
ieee: S.-S. Byun, J. Jalowy, Y.-W. Lee, and G. Schehr, “Moderate-to-large deviation
asymptotics for real eigenvalues of the elliptic Ginibre matrices,” arXiv:2511.09191.
2025.
mla: Byun, Sung-Soo, et al. “Moderate-to-Large Deviation Asymptotics for Real Eigenvalues
of the Elliptic Ginibre Matrices.” ArXiv:2511.09191, 2025.
short: S.-S. Byun, J. Jalowy, Y.-W. Lee, G. Schehr, ArXiv:2511.09191 (2025).
date_created: 2025-12-22T08:37:02Z
date_updated: 2025-12-22T08:37:35Z
department:
- _id: '94'
external_id:
arxiv:
- '2511.09191'
language:
- iso: eng
publication: arXiv:2511.09191
status: public
title: Moderate-to-large deviation asymptotics for real eigenvalues of the elliptic
Ginibre matrices
type: preprint
user_id: '113768'
year: '2025'
...
---
_id: '63393'
abstract:
- lang: eng
text: 'We study the evolution of zeros of high polynomial powers under the heat
flow. For any fixed polynomial $P(z)$, we prove that the empirical zero distribution
of its heat-evolved $n$-th power converges to a distribution on the complex plane
as $n$ tends to infinity. We describe this limit distribution $μ_t$ as a function
of the time parameter $t$ of the heat evolution: For small time, zeros start to
spread out in approximately semicircular distributions, then intricate curves
start to form and merge, until for large time, the zero distribution approaches
a widespread semicircle law through the initial center of mass. The Stieltjes
transform of the limit distribution $μ_t$ satisfies a self-consistent equation
and a Burgers'' equation. The present paper deals with general complex-rooted
polynomials for which, in contrast to the real-rooted case, no free-probabilistic
representation for $μ_t$ is available.'
author:
- first_name: Antonia
full_name: Höfert, Antonia
last_name: Höfert
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Zakhar
full_name: Kabluchko, Zakhar
last_name: Kabluchko
citation:
ama: Höfert A, Jalowy J, Kabluchko Z. Zeros of polynomial powers under the heat
flow. arXiv:251217808. Published online 2025.
apa: Höfert, A., Jalowy, J., & Kabluchko, Z. (2025). Zeros of polynomial powers
under the heat flow. In arXiv:2512.17808.
bibtex: '@article{Höfert_Jalowy_Kabluchko_2025, title={Zeros of polynomial powers
under the heat flow}, journal={arXiv:2512.17808}, author={Höfert, Antonia and
Jalowy, Jonas and Kabluchko, Zakhar}, year={2025} }'
chicago: Höfert, Antonia, Jonas Jalowy, and Zakhar Kabluchko. “Zeros of Polynomial
Powers under the Heat Flow.” ArXiv:2512.17808, 2025.
ieee: A. Höfert, J. Jalowy, and Z. Kabluchko, “Zeros of polynomial powers under
the heat flow,” arXiv:2512.17808. 2025.
mla: Höfert, Antonia, et al. “Zeros of Polynomial Powers under the Heat Flow.” ArXiv:2512.17808,
2025.
short: A. Höfert, J. Jalowy, Z. Kabluchko, ArXiv:2512.17808 (2025).
date_created: 2025-12-22T08:36:24Z
date_updated: 2025-12-22T08:36:46Z
department:
- _id: '94'
external_id:
arxiv:
- '2512.17808'
language:
- iso: eng
publication: arXiv:2512.17808
status: public
title: Zeros of polynomial powers under the heat flow
type: preprint
user_id: '113768'
year: '2025'
...
---
_id: '59188'
author:
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Zakhar
full_name: Kabluchko, Zakhar
last_name: Kabluchko
- first_name: Matthias
full_name: Löwe, Matthias
last_name: Löwe
- first_name: Alexander
full_name: Marynych, Alexander
last_name: Marynych
citation:
ama: Jalowy J, Kabluchko Z, Löwe M, Marynych A. When does the chaos in the Curie-Weiss
model stop to propagate? Electronic Journal of Probability. 2023;28(none).
doi:10.1214/23-ejp1039
apa: Jalowy, J., Kabluchko, Z., Löwe, M., & Marynych, A. (2023). When does the
chaos in the Curie-Weiss model stop to propagate? Electronic Journal of Probability,
28(none). https://doi.org/10.1214/23-ejp1039
bibtex: '@article{Jalowy_Kabluchko_Löwe_Marynych_2023, title={When does the chaos
in the Curie-Weiss model stop to propagate?}, volume={28}, DOI={10.1214/23-ejp1039},
number={none}, journal={Electronic Journal of Probability}, publisher={Institute
of Mathematical Statistics}, author={Jalowy, Jonas and Kabluchko, Zakhar and Löwe,
Matthias and Marynych, Alexander}, year={2023} }'
chicago: Jalowy, Jonas, Zakhar Kabluchko, Matthias Löwe, and Alexander Marynych.
“When Does the Chaos in the Curie-Weiss Model Stop to Propagate?” Electronic
Journal of Probability 28, no. none (2023). https://doi.org/10.1214/23-ejp1039.
ieee: 'J. Jalowy, Z. Kabluchko, M. Löwe, and A. Marynych, “When does the chaos in
the Curie-Weiss model stop to propagate?,” Electronic Journal of Probability,
vol. 28, no. none, 2023, doi: 10.1214/23-ejp1039.'
mla: Jalowy, Jonas, et al. “When Does the Chaos in the Curie-Weiss Model Stop to
Propagate?” Electronic Journal of Probability, vol. 28, no. none, Institute
of Mathematical Statistics, 2023, doi:10.1214/23-ejp1039.
short: J. Jalowy, Z. Kabluchko, M. Löwe, A. Marynych, Electronic Journal of Probability
28 (2023).
date_created: 2025-03-31T07:15:02Z
date_updated: 2025-04-23T14:36:13Z
doi: 10.1214/23-ejp1039
intvolume: ' 28'
issue: none
language:
- iso: eng
publication: Electronic Journal of Probability
publication_identifier:
issn:
- 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
status: public
title: When does the chaos in the Curie-Weiss model stop to propagate?
type: journal_article
user_id: '113768'
volume: 28
year: '2023'
...
---
_id: '59209'
abstract:
- lang: eng
text: "We start with a random polynomial $P^{N}$ of degree $N$ with independent\r\ncoefficients
and consider a new polynomial $P_{t}^{N}$ obtained by repeated\r\napplications
of a fraction differential operator of the form $z^{a}%\r\n(d/dz)^{b},$ where
$a$ and $b$ are real numbers. When $b>0,$ we compute the\r\nlimiting root distribution
$\\mu_{t}$ of $P_{t}^{N}$ as $N\\rightarrow\\infty.$ We\r\nshow that $\\mu_{t}$
is the push-forward of the limiting root distribution of\r\n$P^{N}$ under a transport
map $T_{t}$. The map $T_{t}$ is defined by flowing\r\nalong the characteristic
curves of the PDE satisfied by the log potential of\r\n$\\mu_{t}.$ In the special
case of repeated differentiation, our results may be\r\ninterpreted as saying
that the roots evolve radially \\textit{with constant\r\nspeed} until they hit
the origin, at which point, they cease to exist. For\r\ngeneral $a$ and $b,$ the
transport map $T_{t}$ has a free probability\r\ninterpretation as multiplication
of an $R$-diagonal operator by an $R$-diagonal\r\n\"transport operator.\" As an
application, we obtain a push-forward\r\ncharacterization of the free self-convolution
semigroup $\\oplus$ of radial\r\nmeasures on $\\mathbb{C}$.\r\n We also consider
the case $b<0,$ which includes the case of repeated\r\nintegration. More complicated
behavior of the roots can occur in this case."
author:
- first_name: Brian C.
full_name: Hall, Brian C.
last_name: Hall
- first_name: Ching-Wei
full_name: Ho, Ching-Wei
last_name: Ho
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Zakhar
full_name: Kabluchko, Zakhar
last_name: Kabluchko
citation:
ama: Hall BC, Ho C-W, Jalowy J, Kabluchko Z. Roots of polynomials under repeated
differentiation and repeated applications of fractional differential operators.
arXiv:231214883. Published online 2023.
apa: Hall, B. C., Ho, C.-W., Jalowy, J., & Kabluchko, Z. (2023). Roots of polynomials
under repeated differentiation and repeated applications of fractional differential
operators. In arXiv:2312.14883.
bibtex: '@article{Hall_Ho_Jalowy_Kabluchko_2023, title={Roots of polynomials under
repeated differentiation and repeated applications of fractional differential
operators}, journal={arXiv:2312.14883}, author={Hall, Brian C. and Ho, Ching-Wei
and Jalowy, Jonas and Kabluchko, Zakhar}, year={2023} }'
chicago: Hall, Brian C., Ching-Wei Ho, Jonas Jalowy, and Zakhar Kabluchko. “Roots
of Polynomials under Repeated Differentiation and Repeated Applications of Fractional
Differential Operators.” ArXiv:2312.14883, 2023.
ieee: B. C. Hall, C.-W. Ho, J. Jalowy, and Z. Kabluchko, “Roots of polynomials under
repeated differentiation and repeated applications of fractional differential
operators,” arXiv:2312.14883. 2023.
mla: Hall, Brian C., et al. “Roots of Polynomials under Repeated Differentiation
and Repeated Applications of Fractional Differential Operators.” ArXiv:2312.14883,
2023.
short: B.C. Hall, C.-W. Ho, J. Jalowy, Z. Kabluchko, ArXiv:2312.14883 (2023).
date_created: 2025-03-31T07:15:40Z
date_updated: 2025-04-23T14:38:56Z
external_id:
arxiv:
- '2312.14883'
language:
- iso: eng
publication: arXiv:2312.14883
status: public
title: Roots of polynomials under repeated differentiation and repeated applications
of fractional differential operators
type: preprint
user_id: '113768'
year: '2023'
...
---
_id: '59187'
abstract:
- lang: eng
text: "We investigate the evolution of the empirical distribution of the complex\r\nroots
of high-degree random polynomials, when the polynomial undergoes the heat\r\nflow.
In one prominent example of Weyl polynomials, the limiting zero\r\ndistribution
evolves from the circular law into the elliptic law until it\r\ncollapses to the
Wigner semicircle law, as was recently conjectured for\r\ncharacteristic polynomials
of random matrices by Hall and Ho, 2022. Moreover,\r\nfor a general family of
random polynomials with independent coefficients and\r\nisotropic limiting distribution
of zeros, we determine the zero distribution of\r\nthe heat-evolved polynomials
in terms of its logarithmic potential.\r\nFurthermore, we explicitly identify
two critical time thresholds, at which\r\nsingularities develop and at which the
limiting distribution collapses to the\r\nsemicircle law. We completely characterize
the limiting root distribution of\r\nthe heat-evolved polynomials before singularities
develop as the push-forward\r\nof the initial distribution under a transport map.
Finally, we discuss the\r\nresults from the perspectives of partial differential
equations (in particular\r\nHamilton-Jacobi equation and Burgers' equation), optimal
transport, and free\r\nprobability. The theory is accompanied by explicit examples,
simulations, and\r\nconjectures."
author:
- first_name: Brian C.
full_name: Hall, Brian C.
last_name: Hall
- first_name: Ching-Wei
full_name: Ho, Ching-Wei
last_name: Ho
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Zakhar
full_name: Kabluchko, Zakhar
last_name: Kabluchko
citation:
ama: Hall BC, Ho C-W, Jalowy J, Kabluchko Z. Zeros of random polynomials undergoing
the heat flow. arXiv:230811685. Published online 2023.
apa: Hall, B. C., Ho, C.-W., Jalowy, J., & Kabluchko, Z. (2023). Zeros of random
polynomials undergoing the heat flow. In arXiv:2308.11685.
bibtex: '@article{Hall_Ho_Jalowy_Kabluchko_2023, title={Zeros of random polynomials
undergoing the heat flow}, journal={arXiv:2308.11685}, author={Hall, Brian C.
and Ho, Ching-Wei and Jalowy, Jonas and Kabluchko, Zakhar}, year={2023} }'
chicago: Hall, Brian C., Ching-Wei Ho, Jonas Jalowy, and Zakhar Kabluchko. “Zeros
of Random Polynomials Undergoing the Heat Flow.” ArXiv:2308.11685, 2023.
ieee: B. C. Hall, C.-W. Ho, J. Jalowy, and Z. Kabluchko, “Zeros of random polynomials
undergoing the heat flow,” arXiv:2308.11685. 2023.
mla: Hall, Brian C., et al. “Zeros of Random Polynomials Undergoing the Heat Flow.”
ArXiv:2308.11685, 2023.
short: B.C. Hall, C.-W. Ho, J. Jalowy, Z. Kabluchko, ArXiv:2308.11685 (2023).
date_created: 2025-03-31T07:14:23Z
date_updated: 2025-04-23T14:38:41Z
external_id:
arxiv:
- '2308.11685'
language:
- iso: eng
publication: arXiv:2308.11685
status: public
title: Zeros of random polynomials undergoing the heat flow
type: preprint
user_id: '113768'
year: '2023'
...
---
_id: '59211'
abstract:
- lang: eng
text: "We develop a theory of optimal transport for stationary random measures with\r\na
focus on stationary point processes and construct a family of distances on\r\nthe
set of stationary random measures. These induce a natural notion of\r\ninterpolation
between two stationary random measures along a shortest curve\r\nconnecting them.
In the setting of stationary point processes we leverage this\r\ntransport distance
to give a geometric interpretation for the evolution of\r\ninfinite particle systems
with stationary distribution. Namely, we characterise\r\nthe evolution of infinitely
many Brownian motions as the gradient flow of the\r\nspecific relative entropy
w.r.t.~the Poisson point process. Further, we\r\nestablish displacement convexity
of the specific relative entropy along optimal\r\ninterpolations of point processes
and establish an stationary analogue of the\r\nHWI inequality, relating specific
entropy, transport distance, and a specific\r\nrelative Fisher information."
author:
- first_name: Matthias
full_name: Erbar, Matthias
last_name: Erbar
- first_name: Martin
full_name: Huesmann, Martin
last_name: Huesmann
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Bastian
full_name: Müller, Bastian
last_name: Müller
citation:
ama: 'Erbar M, Huesmann M, Jalowy J, Müller B. Optimal transport of stationary point
processes: Metric structure, gradient flow and convexity of the specific entropy.
arXiv:230411145. Published online 2023.'
apa: 'Erbar, M., Huesmann, M., Jalowy, J., & Müller, B. (2023). Optimal transport
of stationary point processes: Metric structure, gradient flow and convexity
of the specific entropy. In arXiv:2304.11145.'
bibtex: '@article{Erbar_Huesmann_Jalowy_Müller_2023, title={Optimal transport of
stationary point processes: Metric structure, gradient flow and convexity of
the specific entropy}, journal={arXiv:2304.11145}, author={Erbar, Matthias and
Huesmann, Martin and Jalowy, Jonas and Müller, Bastian}, year={2023} }'
chicago: 'Erbar, Matthias, Martin Huesmann, Jonas Jalowy, and Bastian Müller. “Optimal
Transport of Stationary Point Processes: Metric Structure, Gradient Flow and
Convexity of the Specific Entropy.” ArXiv:2304.11145, 2023.'
ieee: 'M. Erbar, M. Huesmann, J. Jalowy, and B. Müller, “Optimal transport of stationary
point processes: Metric structure, gradient flow and convexity of the specific
entropy,” arXiv:2304.11145. 2023.'
mla: 'Erbar, Matthias, et al. “Optimal Transport of Stationary Point Processes:
Metric Structure, Gradient Flow and Convexity of the Specific Entropy.” ArXiv:2304.11145,
2023.'
short: M. Erbar, M. Huesmann, J. Jalowy, B. Müller, ArXiv:2304.11145 (2023).
date_created: 2025-03-31T07:16:09Z
date_updated: 2025-04-23T14:39:08Z
external_id:
arxiv:
- '2304.11145'
language:
- iso: eng
publication: arXiv:2304.11145
status: public
title: 'Optimal transport of stationary point processes: Metric structure, gradient
flow and convexity of the specific entropy'
type: preprint
user_id: '113768'
year: '2023'
...
---
_id: '59189'
abstract:
- lang: eng
text: "We develop a theory of optimal transport for stationary random measures with\r\na
focus on stationary point processes and construct a family of distances on\r\nthe
set of stationary random measures. These induce a natural notion of\r\ninterpolation
between two stationary random measures along a shortest curve\r\nconnecting them.
In the setting of stationary point processes we leverage this\r\ntransport distance
to give a geometric interpretation for the evolution of\r\ninfinite particle systems
with stationary distribution. Namely, we characterise\r\nthe evolution of infinitely
many Brownian motions as the gradient flow of the\r\nspecific relative entropy
w.r.t.~the Poisson point process. Further, we\r\nestablish displacement convexity
of the specific relative entropy along optimal\r\ninterpolations of point processes
and establish an stationary analogue of the\r\nHWI inequality, relating specific
entropy, transport distance, and a specific\r\nrelative Fisher information."
author:
- first_name: Matthias
full_name: Erbar, Matthias
last_name: Erbar
- first_name: Martin
full_name: Huesmann, Martin
last_name: Huesmann
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Bastian
full_name: Müller, Bastian
last_name: Müller
citation:
ama: 'Erbar M, Huesmann M, Jalowy J, Müller B. Optimal transport of stationary point
processes: Metric structure, gradient flow and convexity of the specific entropy.
arXiv:230411145. Published online 2023.'
apa: 'Erbar, M., Huesmann, M., Jalowy, J., & Müller, B. (2023). Optimal transport
of stationary point processes: Metric structure, gradient flow and convexity
of the specific entropy. In arXiv:2304.11145.'
bibtex: '@article{Erbar_Huesmann_Jalowy_Müller_2023, title={Optimal transport of
stationary point processes: Metric structure, gradient flow and convexity of
the specific entropy}, journal={arXiv:2304.11145}, author={Erbar, Matthias and
Huesmann, Martin and Jalowy, Jonas and Müller, Bastian}, year={2023} }'
chicago: 'Erbar, Matthias, Martin Huesmann, Jonas Jalowy, and Bastian Müller. “Optimal
Transport of Stationary Point Processes: Metric Structure, Gradient Flow and
Convexity of the Specific Entropy.” ArXiv:2304.11145, 2023.'
ieee: 'M. Erbar, M. Huesmann, J. Jalowy, and B. Müller, “Optimal transport of stationary
point processes: Metric structure, gradient flow and convexity of the specific
entropy,” arXiv:2304.11145. 2023.'
mla: 'Erbar, Matthias, et al. “Optimal Transport of Stationary Point Processes:
Metric Structure, Gradient Flow and Convexity of the Specific Entropy.” ArXiv:2304.11145,
2023.'
short: M. Erbar, M. Huesmann, J. Jalowy, B. Müller, ArXiv:2304.11145 (2023).
date_created: 2025-03-31T07:15:22Z
date_updated: 2025-04-23T14:38:52Z
external_id:
arxiv:
- '2304.11145'
language:
- iso: eng
publication: arXiv:2304.11145
status: public
title: 'Optimal transport of stationary point processes: Metric structure, gradient
flow and convexity of the specific entropy'
type: preprint
user_id: '113768'
year: '2023'
...
---
_id: '59184'
author:
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
citation:
ama: Jalowy J. The Wasserstein distance to the circular law. Annales de l’Institut
Henri Poincaré, Probabilités et Statistiques. 2023;59(4). doi:10.1214/22-aihp1317
apa: Jalowy, J. (2023). The Wasserstein distance to the circular law. Annales
de l’Institut Henri Poincaré, Probabilités et Statistiques, 59(4).
https://doi.org/10.1214/22-aihp1317
bibtex: '@article{Jalowy_2023, title={The Wasserstein distance to the circular law},
volume={59}, DOI={10.1214/22-aihp1317},
number={4}, journal={Annales de l’Institut Henri Poincaré, Probabilités et Statistiques},
publisher={Institute of Mathematical Statistics}, author={Jalowy, Jonas}, year={2023}
}'
chicago: Jalowy, Jonas. “The Wasserstein Distance to the Circular Law.” Annales
de l’Institut Henri Poincaré, Probabilités et Statistiques 59, no. 4 (2023).
https://doi.org/10.1214/22-aihp1317.
ieee: 'J. Jalowy, “The Wasserstein distance to the circular law,” Annales de
l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 59, no. 4, 2023,
doi: 10.1214/22-aihp1317.'
mla: Jalowy, Jonas. “The Wasserstein Distance to the Circular Law.” Annales de
l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 59, no. 4, Institute
of Mathematical Statistics, 2023, doi:10.1214/22-aihp1317.
short: J. Jalowy, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques
59 (2023).
date_created: 2025-03-31T07:12:40Z
date_updated: 2025-04-23T14:38:24Z
doi: 10.1214/22-aihp1317
intvolume: ' 59'
issue: '4'
language:
- iso: eng
publication: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
status: public
title: The Wasserstein distance to the circular law
type: journal_article
user_id: '113768'
volume: 59
year: '2023'
...
---
_id: '59210'
abstract:
- lang: eng
text: "We establish basic properties of the heat flow on entire holomorphic\r\nfunctions
that have order at most 2. We then look specifically at the action of\r\nthe heat
flow on the Gaussian analytic function (GAF). We show that applying\r\nthe heat
flow to a GAF and then rescaling and multiplying by an exponential of\r\na quadratic
function gives another GAF. It follows that the zeros of the GAF\r\nare invariant
in distribution under the heat flow, up to a simple rescaling.\r\n We then show
that the zeros of the GAF evolve under the heat flow\r\napproximately along straight
lines, with an error whose distribution is\r\nindependent of the starting point.
Finally, we connect the heat flow on the GAF\r\nto the metaplectic representation
of the double cover of the group\r\n$SL(2;\\mathbb{R}).$"
author:
- first_name: Brian
full_name: Hall, Brian
last_name: Hall
- first_name: Ching-Wei
full_name: Ho, Ching-Wei
last_name: Ho
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Zakhar
full_name: Kabluchko, Zakhar
last_name: Kabluchko
citation:
ama: Hall B, Ho C-W, Jalowy J, Kabluchko Z. The heat flow, GAF, and SL(2;R). arXiv:230406665.
Published online 2023.
apa: Hall, B., Ho, C.-W., Jalowy, J., & Kabluchko, Z. (2023). The heat flow,
GAF, and SL(2;R). In arXiv:2304.06665.
bibtex: '@article{Hall_Ho_Jalowy_Kabluchko_2023, title={The heat flow, GAF, and
SL(2;R)}, journal={arXiv:2304.06665}, author={Hall, Brian and Ho, Ching-Wei and
Jalowy, Jonas and Kabluchko, Zakhar}, year={2023} }'
chicago: Hall, Brian, Ching-Wei Ho, Jonas Jalowy, and Zakhar Kabluchko. “The Heat
Flow, GAF, and SL(2;R).” ArXiv:2304.06665, 2023.
ieee: B. Hall, C.-W. Ho, J. Jalowy, and Z. Kabluchko, “The heat flow, GAF, and SL(2;R),”
arXiv:2304.06665. 2023.
mla: Hall, Brian, et al. “The Heat Flow, GAF, and SL(2;R).” ArXiv:2304.06665,
2023.
short: B. Hall, C.-W. Ho, J. Jalowy, Z. Kabluchko, ArXiv:2304.06665 (2023).
date_created: 2025-03-31T07:15:53Z
date_updated: 2025-04-23T14:39:00Z
external_id:
arxiv:
- '2304.06665'
language:
- iso: eng
publication: arXiv:2304.06665
status: public
title: The heat flow, GAF, and SL(2;R)
type: preprint
user_id: '113768'
year: '2023'
...
---
_id: '59186'
abstract:
- lang: eng
text: "AbstractIn this note we study the block
spin mean-field Potts model, in which the spins are divided into s
blocks and can take $$q\\ge
2$$\r\n
\ \r\n q\r\n ≥\r\n
\ 2\r\n \r\n
different values (colors). Each block is allowed to contain a different proportion
of vertices and behaves itself like a mean-field Ising/Potts model which also
interacts with other blocks according to different temperatures. Of particular
interest is the behavior of the magnetization, which counts the number of colors
appearing in the distinct blocks. We prove central limit theorems for the magnetization
in the generalized high-temperature regime and provide a moderate deviation principle
for its fluctuations on lower scalings. More precisely, the magnetization concentrates
around the uniform vector of all colors with an explicit, but singular, Gaussian
distribution. In order to remove the singular component, we will also consider
a rotated magnetization, which enables us to compare our results to various related
models."
article_number: '3'
author:
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Matthias
full_name: Löwe, Matthias
last_name: Löwe
- first_name: Holger
full_name: Sambale, Holger
last_name: Sambale
citation:
ama: Jalowy J, Löwe M, Sambale H. Fluctuations of the Magnetization in the Block
Potts Model. Journal of Statistical Physics. 2022;187(1). doi:10.1007/s10955-022-02889-4
apa: Jalowy, J., Löwe, M., & Sambale, H. (2022). Fluctuations of the Magnetization
in the Block Potts Model. Journal of Statistical Physics, 187(1),
Article 3. https://doi.org/10.1007/s10955-022-02889-4
bibtex: '@article{Jalowy_Löwe_Sambale_2022, title={Fluctuations of the Magnetization
in the Block Potts Model}, volume={187}, DOI={10.1007/s10955-022-02889-4},
number={13}, journal={Journal of Statistical Physics}, publisher={Springer Science
and Business Media LLC}, author={Jalowy, Jonas and Löwe, Matthias and Sambale,
Holger}, year={2022} }'
chicago: Jalowy, Jonas, Matthias Löwe, and Holger Sambale. “Fluctuations of the
Magnetization in the Block Potts Model.” Journal of Statistical Physics
187, no. 1 (2022). https://doi.org/10.1007/s10955-022-02889-4.
ieee: 'J. Jalowy, M. Löwe, and H. Sambale, “Fluctuations of the Magnetization in
the Block Potts Model,” Journal of Statistical Physics, vol. 187, no. 1,
Art. no. 3, 2022, doi: 10.1007/s10955-022-02889-4.'
mla: Jalowy, Jonas, et al. “Fluctuations of the Magnetization in the Block Potts
Model.” Journal of Statistical Physics, vol. 187, no. 1, 3, Springer Science
and Business Media LLC, 2022, doi:10.1007/s10955-022-02889-4.
short: J. Jalowy, M. Löwe, H. Sambale, Journal of Statistical Physics 187 (2022).
date_created: 2025-03-31T07:14:09Z
date_updated: 2025-04-23T14:38:45Z
doi: 10.1007/s10955-022-02889-4
intvolume: ' 187'
issue: '1'
language:
- iso: eng
publication: Journal of Statistical Physics
publication_identifier:
issn:
- 0022-4715
- 1572-9613
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Fluctuations of the Magnetization in the Block Potts Model
type: journal_article
user_id: '113768'
volume: 187
year: '2022'
...
---
_id: '59185'
author:
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
citation:
ama: Jalowy J. Rate of convergence for products of independent non-Hermitian random
matrices. Electronic Journal of Probability. 2021;26(none). doi:10.1214/21-ejp625
apa: Jalowy, J. (2021). Rate of convergence for products of independent non-Hermitian
random matrices. Electronic Journal of Probability, 26(none). https://doi.org/10.1214/21-ejp625
bibtex: '@article{Jalowy_2021, title={Rate of convergence for products of independent
non-Hermitian random matrices}, volume={26}, DOI={10.1214/21-ejp625},
number={none}, journal={Electronic Journal of Probability}, publisher={Institute
of Mathematical Statistics}, author={Jalowy, Jonas}, year={2021} }'
chicago: Jalowy, Jonas. “Rate of Convergence for Products of Independent Non-Hermitian
Random Matrices.” Electronic Journal of Probability 26, no. none (2021).
https://doi.org/10.1214/21-ejp625.
ieee: 'J. Jalowy, “Rate of convergence for products of independent non-Hermitian
random matrices,” Electronic Journal of Probability, vol. 26, no. none,
2021, doi: 10.1214/21-ejp625.'
mla: Jalowy, Jonas. “Rate of Convergence for Products of Independent Non-Hermitian
Random Matrices.” Electronic Journal of Probability, vol. 26, no. none,
Institute of Mathematical Statistics, 2021, doi:10.1214/21-ejp625.
short: J. Jalowy, Electronic Journal of Probability 26 (2021).
date_created: 2025-03-31T07:13:44Z
date_updated: 2025-04-23T14:38:37Z
doi: 10.1214/21-ejp625
intvolume: ' 26'
issue: none
language:
- iso: eng
publication: Electronic Journal of Probability
publication_identifier:
issn:
- 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
status: public
title: Rate of convergence for products of independent non-Hermitian random matrices
type: journal_article
user_id: '113768'
volume: 26
year: '2021'
...
---
_id: '59214'
author:
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
- first_name: Matthias
full_name: Löwe, Matthias
last_name: Löwe
citation:
ama: Jalowy J, Löwe M. Reconstructing a recurrent random environment from a single
trajectory of a Random Walk in Random Environment with errors. Electronic Communications
in Probability. 2021;26(none). doi:10.1214/21-ecp425
apa: Jalowy, J., & Löwe, M. (2021). Reconstructing a recurrent random environment
from a single trajectory of a Random Walk in Random Environment with errors. Electronic
Communications in Probability, 26(none). https://doi.org/10.1214/21-ecp425
bibtex: '@article{Jalowy_Löwe_2021, title={Reconstructing a recurrent random environment
from a single trajectory of a Random Walk in Random Environment with errors},
volume={26}, DOI={10.1214/21-ecp425},
number={none}, journal={Electronic Communications in Probability}, publisher={Institute
of Mathematical Statistics}, author={Jalowy, Jonas and Löwe, Matthias}, year={2021}
}'
chicago: Jalowy, Jonas, and Matthias Löwe. “Reconstructing a Recurrent Random Environment
from a Single Trajectory of a Random Walk in Random Environment with Errors.”
Electronic Communications in Probability 26, no. none (2021). https://doi.org/10.1214/21-ecp425.
ieee: 'J. Jalowy and M. Löwe, “Reconstructing a recurrent random environment from
a single trajectory of a Random Walk in Random Environment with errors,” Electronic
Communications in Probability, vol. 26, no. none, 2021, doi: 10.1214/21-ecp425.'
mla: Jalowy, Jonas, and Matthias Löwe. “Reconstructing a Recurrent Random Environment
from a Single Trajectory of a Random Walk in Random Environment with Errors.”
Electronic Communications in Probability, vol. 26, no. none, Institute
of Mathematical Statistics, 2021, doi:10.1214/21-ecp425.
short: J. Jalowy, M. Löwe, Electronic Communications in Probability 26 (2021).
date_created: 2025-03-31T07:17:34Z
date_updated: 2025-04-23T14:39:18Z
doi: 10.1214/21-ecp425
intvolume: ' 26'
issue: none
language:
- iso: eng
publication: Electronic Communications in Probability
publication_identifier:
issn:
- 1083-589X
publication_status: published
publisher: Institute of Mathematical Statistics
status: public
title: Reconstructing a recurrent random environment from a single trajectory of a
Random Walk in Random Environment with errors
type: journal_article
user_id: '113768'
volume: 26
year: '2021'
...
---
_id: '59183'
abstract:
- lang: eng
text: ' The aim of this paper is to investigate the Kolmogorov distance
of the Circular Law to the empirical spectral distribution of non-Hermitian random
matrices with independent entries. The optimal rate of convergence is determined
by the Ginibre ensemble and is given by [Formula: see text]. A smoothing inequality
for complex measures that quantitatively relates the uniform Kolmogorov-like distance
to the concentration of logarithmic potentials is shown. Combining it with results
from Local Circular Laws, we apply it to prove nearly optimal rate of convergence
to the Circular Law in Kolmogorov distance. Furthermore, we show that the same
rate of convergence holds for the empirical measure of the roots of Weyl random
polynomials. '
article_number: '2150026'
author:
- first_name: Friedrich
full_name: Götze, Friedrich
last_name: Götze
- first_name: Jonas
full_name: Jalowy, Jonas
id: '113768'
last_name: Jalowy
orcid: 0000-0001-9624-2685
citation:
ama: 'Götze F, Jalowy J. Rate of convergence to the Circular Law via smoothing inequalities
for log-potentials. Random Matrices: Theory and Applications. 2020;10(03).
doi:10.1142/s201032632150026x'
apa: 'Götze, F., & Jalowy, J. (2020). Rate of convergence to the Circular Law
via smoothing inequalities for log-potentials. Random Matrices: Theory and
Applications, 10(03), Article 2150026. https://doi.org/10.1142/s201032632150026x'
bibtex: '@article{Götze_Jalowy_2020, title={Rate of convergence to the Circular
Law via smoothing inequalities for log-potentials}, volume={10}, DOI={10.1142/s201032632150026x},
number={032150026}, journal={Random Matrices: Theory and Applications}, publisher={World
Scientific Pub Co Pte Lt}, author={Götze, Friedrich and Jalowy, Jonas}, year={2020}
}'
chicago: 'Götze, Friedrich, and Jonas Jalowy. “Rate of Convergence to the Circular
Law via Smoothing Inequalities for Log-Potentials.” Random Matrices: Theory
and Applications 10, no. 03 (2020). https://doi.org/10.1142/s201032632150026x.'
ieee: 'F. Götze and J. Jalowy, “Rate of convergence to the Circular Law via smoothing
inequalities for log-potentials,” Random Matrices: Theory and Applications,
vol. 10, no. 03, Art. no. 2150026, 2020, doi: 10.1142/s201032632150026x.'
mla: 'Götze, Friedrich, and Jonas Jalowy. “Rate of Convergence to the Circular Law
via Smoothing Inequalities for Log-Potentials.” Random Matrices: Theory and
Applications, vol. 10, no. 03, 2150026, World Scientific Pub Co Pte Lt, 2020,
doi:10.1142/s201032632150026x.'
short: 'F. Götze, J. Jalowy, Random Matrices: Theory and Applications 10 (2020).'
date_created: 2025-03-31T07:12:18Z
date_updated: 2025-04-23T14:38:18Z
doi: 10.1142/s201032632150026x
intvolume: ' 10'
issue: '03'
language:
- iso: eng
publication: 'Random Matrices: Theory and Applications'
publication_identifier:
issn:
- 2010-3263
- 2010-3271
publication_status: published
publisher: World Scientific Pub Co Pte Lt
status: public
title: Rate of convergence to the Circular Law via smoothing inequalities for log-potentials
type: journal_article
user_id: '113768'
volume: 10
year: '2020'
...