Analyticity of the entropy for some random walks

TL;DR

This paper proves that for certain random walks on free groups, the entropy and linear drift change smoothly and analytically as the probabilities of steps are varied, revealing deep mathematical properties.

Contribution

It establishes the analyticity of entropy and drift functions for non-degenerate, finitely supported random walks on free groups, a novel theoretical insight.

Findings

Entropy varies analytically with step probabilities.

Linear drift varies analytically with step probabilities.

Provides mathematical foundation for understanding random walk behaviors.

Abstract

We consider non-degenerate, finitely supported random walks on a free group. We show that the entropy and the linear drift vary analytically with th eprobability of constant support.