---
_id: '65232'
abstract:
- lang: eng
  text: On finite regular graphs, we construct Patterson-Sullivan distributions associated
    with eigenfunctions of the discrete Laplace operator via their boundary values
    on the phase space. These distributions are closely related to Wigner distributions
    defined via a pseudo-differential calculus on graphs, which appear naturally in
    the study of quantum chaos. Using a pairing formula, we prove that Patterson-Sullivan
    distributions are also related to invariant Ruelle distributions arising from
    the transfer operator of the geodesic flow on the shift space. Both relationships
    provide discrete analogues of results for compact hyperbolic surfaces obtained
    by Anantharaman-Zelditch and by Guillarmou-Hilgert-Weich.
author:
- first_name: Christian
  full_name: Arends, Christian
  last_name: Arends
- first_name: Guendalina
  full_name: Palmirotta, Guendalina
  id: '109467'
  last_name: Palmirotta
citation:
  ama: Arends C, Palmirotta G. Patterson-Sullivan distributions of finite regular
    graphs. <i>arXiv:260309779</i>. Published online 2026.
  apa: Arends, C., &#38; Palmirotta, G. (2026). Patterson-Sullivan distributions of
    finite regular graphs. In <i>arXiv:2603.09779</i>.
  bibtex: '@article{Arends_Palmirotta_2026, title={Patterson-Sullivan distributions
    of finite regular graphs}, journal={arXiv:2603.09779}, author={Arends, Christian
    and Palmirotta, Guendalina}, year={2026} }'
  chicago: Arends, Christian, and Guendalina Palmirotta. “Patterson-Sullivan Distributions
    of Finite Regular Graphs.” <i>ArXiv:2603.09779</i>, 2026.
  ieee: C. Arends and G. Palmirotta, “Patterson-Sullivan distributions of finite regular
    graphs,” <i>arXiv:2603.09779</i>. 2026.
  mla: Arends, Christian, and Guendalina Palmirotta. “Patterson-Sullivan Distributions
    of Finite Regular Graphs.” <i>ArXiv:2603.09779</i>, 2026.
  short: C. Arends, G. Palmirotta, ArXiv:2603.09779 (2026).
date_created: 2026-03-30T11:56:04Z
date_updated: 2026-03-30T12:02:56Z
department:
- _id: '548'
- _id: '10'
- _id: '34'
external_id:
  arxiv:
  - '2603.09779'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2603.09779
oa: '1'
page: '38'
project:
- _id: '358'
  name: 'TRR 358; TP B04:  Geodätische Flüsse und Weyl Kammer Flüsse auf affinen Gebäuden'
publication: arXiv:2603.09779
status: public
title: Patterson-Sullivan distributions of finite regular graphs
type: preprint
user_id: '109467'
year: '2026'
...
---
_id: '32097'
author:
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Yannick
  full_name: Guedes Bonthonneau, Yannick
  last_name: Guedes Bonthonneau
- first_name: Colin
  full_name: Guillarmou, Colin
  last_name: Guillarmou
citation:
  ama: 'Weich T, Guedes Bonthonneau Y, Guillarmou C. SRB Measures of Anosov Actions.
    <i>Journal of Differential Geometry</i>. 2024;128:959-1026. doi:<a href="https://doi.org/
    DOI: 10.4310/jdg/1729092452"> DOI: 10.4310/jdg/1729092452</a>'
  apa: 'Weich, T., Guedes Bonthonneau, Y., &#38; Guillarmou, C. (2024). SRB Measures
    of Anosov Actions. <i>Journal of Differential Geometry</i>, <i>128</i>, 959–1026.
    <a href="https://doi.org/ DOI: 10.4310/jdg/1729092452">https://doi.org/ DOI: 10.4310/jdg/1729092452</a>'
  bibtex: '@article{Weich_Guedes Bonthonneau_Guillarmou_2024, title={SRB Measures
    of Anosov Actions}, volume={128}, DOI={<a href="https://doi.org/ DOI: 10.4310/jdg/1729092452">
    DOI: 10.4310/jdg/1729092452</a>}, journal={Journal of Differential Geometry},
    author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin},
    year={2024}, pages={959–1026} }'
  chicago: 'Weich, Tobias, Yannick Guedes Bonthonneau, and Colin Guillarmou. “SRB
    Measures of Anosov Actions.” <i>Journal of Differential Geometry</i> 128 (2024):
    959–1026. <a href="https://doi.org/ DOI: 10.4310/jdg/1729092452">https://doi.org/
    DOI: 10.4310/jdg/1729092452</a>.'
  ieee: 'T. Weich, Y. Guedes Bonthonneau, and C. Guillarmou, “SRB Measures of Anosov
    Actions,” <i>Journal of Differential Geometry</i>, vol. 128, pp. 959–1026, 2024,
    doi: <a href="https://doi.org/ DOI: 10.4310/jdg/1729092452"> DOI: 10.4310/jdg/1729092452</a>.'
  mla: 'Weich, Tobias, et al. “SRB Measures of Anosov Actions.” <i>Journal of Differential
    Geometry</i>, vol. 128, 2024, pp. 959–1026, doi:<a href="https://doi.org/ DOI:
    10.4310/jdg/1729092452"> DOI: 10.4310/jdg/1729092452</a>.'
  short: T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry
    128 (2024) 959–1026.
date_created: 2022-06-22T09:56:23Z
date_updated: 2025-01-02T15:39:43Z
ddc:
- '510'
department:
- _id: '10'
- _id: '623'
- _id: '548'
doi: ' DOI: 10.4310/jdg/1729092452'
external_id:
  arxiv:
  - https://arxiv.org/abs/2103.12127
file:
- access_level: open_access
  content_type: application/pdf
  creator: weich
  date_created: 2022-06-22T09:56:08Z
  date_updated: 2022-06-22T09:56:08Z
  file_id: '32098'
  file_name: 2103.12127.pdf
  file_size: 745870
  relation: main_file
file_date_updated: 2022-06-22T09:56:08Z
has_accepted_license: '1'
intvolume: '       128'
language:
- iso: eng
oa: '1'
page: 959-1026
project:
- _id: '358'
  grant_number: '491392403'
  name: TRR 358 - Geodätische Flüsse und Weyl Kammer Flüsse auf affinen Gebäuden (Teilprojekt
    B04)
- _id: '355'
  grant_number: '422642921'
  name: Mikrolokale Methoden für hyperbolische Dynamiken
publication: Journal of Differential Geometry
status: public
title: SRB Measures of Anosov Actions
type: journal_article
user_id: '49178'
volume: 128
year: '2024'
...