Peripheral Poisson boundaries and jointly bi-harmonic functions

2023/07/21 by Das, Sayan
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2307.11295

Abstract

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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