Peripheral Poisson boundaries and jointly bi-harmonic functions
arXiv (Cornell University)(2023)
摘要
In this paper we answer a question of Kaimanovich by characterizing (jointly) bi-harmonic functions on countable, discrete groups with respect to a symmetric, generating measure. We also study the peripheral Poisson boundary of $L(\G)$ with respect to Markov operators arising from symmetric, generating probability measures on a countable, discrete group $\G$. We solve a recent conjecture of Bhat, Talwar and Kar regarding peripheral eigenvalues and their corresponding eigenvectors for such Markov operators, and provide a complete description of the peripheral Poisson boundary in the aforementioned scenario.
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关键词
poisson,boundaries,bi-harmonic
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