Patterson-Sullivan distributions of finite regular graphs

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Main Authors:	Arends, Christian, Palmirotta, Guendalina
Format:	Preprint
Published:	2026
Subjects:	Spectral Theory Mathematical Physics 37E25, 47B93, 20E08
Online Access:	Acceder al recurso
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_version_	1866908915424296960
author	Arends, Christian Palmirotta, Guendalina
author_facet	Arends, Christian Palmirotta, Guendalina
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2603_09779
institution	arXiv
publishDate	2026
record_format	arxiv
spellingShingle	Patterson-Sullivan distributions of finite regular graphs Arends, Christian Palmirotta, Guendalina Spectral Theory Mathematical Physics 37E25, 47B93, 20E08 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.
title	Patterson-Sullivan distributions of finite regular graphs
topic	Spectral Theory Mathematical Physics 37E25, 47B93, 20E08
url	https://arxiv.org/abs/2603.09779

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