---
_id: '54820'
abstract:
- lang: eng
text: "We study the asymptotic behaviour of Bessel functions associated of root\r\nsystems
of type $A_{n-1}$ and type $B_n$ with positive multiplicities as the\r\nrank $n$
tends to infinity. In both cases, we characterize the possible limit\r\nfunctions
and the Vershik-Kerov type sequences of spectral parameters for which\r\nsuch
limits exist. In the type $A$ case, this gives a new and very natural\r\napproach
to recent results by Assiotis and Najnudel in the context of\r\n$\\beta$-ensembles
in random matrix theory. These results generalize known facts\r\nabout the approximation
of the (positive-definite) Olshanski spherical\r\nfunctions of the space of infinite-dimensional
Hermitian matrices over $\\mathbb\r\nF = \\mathbb R, \\mathbb C, \\mathbb H$ (with
the action of the associated\r\ninfinite unitary group) by spherical functions
of finite-dimensional spaces of\r\nHermitian matrices. In the type B case, our
results include asymptotic results\r\nfor the spherical functions associated with
the Cartan motion groups of\r\nnon-compact Grassmannians as the rank goes to infinity,
and a classification of\r\nthe Olshanski spherical functions of the associated
inductive limits."
author:
- first_name: Dominik
full_name: Brennecken, Dominik
id: '55911'
last_name: Brennecken
- first_name: Margit
full_name: Rösler, Margit
id: '37390'
last_name: Rösler
citation:
ama: Brennecken D, Rösler M. Limits of Bessel functions for root systems as the
rank tends to infinity. *Indagationes Mathematicae*. Published online 2024.
doi:10.1016/j.indag.2024.05.004
apa: Brennecken, D., & Rösler, M. (2024). Limits of Bessel functions for root
systems as the rank tends to infinity. *Indagationes Mathematicae*. https://doi.org/10.1016/j.indag.2024.05.004
bibtex: '@article{Brennecken_Rösler_2024, title={Limits of Bessel functions for
root systems as the rank tends to infinity}, DOI={10.1016/j.indag.2024.05.004},
journal={Indagationes Mathematicae}, publisher={Elsevier}, author={Brennecken,
Dominik and Rösler, Margit}, year={2024} }'
chicago: Brennecken, Dominik, and Margit Rösler. “Limits of Bessel Functions for
Root Systems as the Rank Tends to Infinity.” *Indagationes Mathematicae*,
2024. https://doi.org/10.1016/j.indag.2024.05.004.
ieee: 'D. Brennecken and M. Rösler, “Limits of Bessel functions for root systems
as the rank tends to infinity,” *Indagationes Mathematicae*, 2024, doi:
10.1016/j.indag.2024.05.004.'
mla: Brennecken, Dominik, and Margit Rösler. “Limits of Bessel Functions for Root
Systems as the Rank Tends to Infinity.” *Indagationes Mathematicae*, Elsevier,
2024, doi:10.1016/j.indag.2024.05.004.
short: D. Brennecken, M. Rösler, Indagationes Mathematicae (2024).
date_created: 2024-06-19T08:46:08Z
date_updated: 2024-07-15T09:09:55Z
doi: 10.1016/j.indag.2024.05.004
language:
- iso: eng
publication: Indagationes Mathematicae
publication_status: epub_ahead
publisher: Elsevier
status: public
title: Limits of Bessel functions for root systems as the rank tends to infinity
type: journal_article
user_id: '82981'
year: '2024'
...