Patterson-Sullivan distributions of finite regular graphs
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908915424296960 |
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| 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 |
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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 |