Liouville property and poisson boundary of random walks with infinite entropy: what's amiss?

Vadim Kaimanovich

Department of Mathematics and Statistics, University of Ottawa, Canada

Abstract: We discuss the qualitatively new properties of random walks on groups that arise in the situation when the entropy of the step distribution is infinite.

Keywords: random walk, asymptotic entropy, Liouville property, Poisson boundary.

MSC: 28D20, 37A50, 43A07, 60J50

Received: 30.12.2023
Accepted: 18.01.2024

DOI: 10.4213/faa4191

 English version: Functional Analysis and Its Applications, 2024, 58:2, 160–181

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