Property A and the existence of a Markov process with a trivial Poisson boundary

TL;DR

This paper shows that property A for a space is equivalent to the existence of a Markov process with a trivial Poisson boundary, linking geometric property to probabilistic behavior.

Contribution

It establishes an equivalence between property A and the existence of a Markov process with a trivial Poisson boundary, providing a new perspective on property A.

Findings

Property A is equivalent to the existence of a Markov process with a trivial Poisson boundary.

This equivalence offers a probabilistic characterization of property A.

The result connects geometric and probabilistic properties of spaces.

Abstract

This note make the observation that property A for a space is equivalent to the existence of a Markov process on the space which has a (uniformly) trivial Poisson boundary.