有限正则图上的Patterson-Sullivan分布
Patterson-Sullivan distributions of finite regular graphs
AI总结：
研究有限正则图上通过相空间边界值构造Patterson-Sullivan分布，揭示其与Wigner分布及不变Ruelle分布的关系，为紧超曲面结果提供离散类比。
摘要：
在有限正则图上，我们通过相空间边界的特征函数值构造Patterson-Sullivan分布，这些分布与通过图上伪微分算子定义的Wigner分布密切相关，后者在量子混沌研究中自然出现。利用配对公式，我们证明Patterson-Sullivan分布也与来自移位空间测地流转移算子的不变Ruelle分布相关。这两种关系为Anantharaman-Zelditch和Guillarmou-Hilgert-Weich在紧超曲面上的结果提供了离散类比。
英文摘要：
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.
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