EVERY EXPONENTIAL GROUP SUPPORTS A POSITIVE HARMONIC FUNCTION

Gideon Amir; Gady Kozma

doi:10.1090/proc/15435

EVERY EXPONENTIAL GROUP SUPPORTS A POSITIVE HARMONIC FUNCTION

Bar-Ilan University, Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that all groups of exponential growth support non-constant positive harmonic functions. In fact, our 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.

Original language	English GB
Pages (from-to)	1-5
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	153
Issue number	1
Early online date	4 Nov 2024
DOIs	https://doi.org/10.1090/proc/15435
State	Published - Jan 2025

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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title = "EVERY EXPONENTIAL GROUP SUPPORTS A POSITIVE HARMONIC FUNCTION",

abstract = "We prove that all groups of exponential growth support non-constant positive harmonic functions. In fact, our 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.",

author = "Gideon Amir and Gady Kozma",

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doi = "10.1090/proc/15435",

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EVERY EXPONENTIAL GROUP SUPPORTS A POSITIVE HARMONIC FUNCTION

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