Every exponential group supports a positive harmonic function

2017/10/31 by Amir, Gideon, Kozma, Gady · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1711.00050

Abstract

We prove that all groups of exponential growth support non-constant positive harmonic functions. In fact, out results hold in the more general case of strongly connected, finitely supported Markov chains invariant under some transitive group of automorphisms for which the directed balls grow exponentially.

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