EVERY EXPONENTIAL GROUP SUPPORTS A POSITIVE HARMONIC FUNCTION

Gideon Amir, Gady Kozma

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)1-5
Number of pages5
JournalProceedings of the American Mathematical Society
Volume153
Issue number1
DOIs
StatePublished - Jan 2025

Bibliographical note

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© 2024 American Mathematical Society.

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