Sharp lower bounds for the asymptotic entropy of symmetric random walks
Probability
2014-02-11 v3
Abstract
The entropy, the spectral radius and the drift are important numerical quantities associated to random walks on countable groups. We prove sharp inequalities relating those quantities for walks with a finite second moment, improving upon previous results of Avez, Varopoulos, Carne, Ledrappier. We also deduce inequalities between these quantities and the volume growth of the group. Finally, we show that the equality case in our inequality is rather rigid.
Keywords
Cite
@article{arxiv.1209.3378,
title = {Sharp lower bounds for the asymptotic entropy of symmetric random walks},
author = {Sébastien Gouëzel and Frédéric Mathéus and François Maucourant},
journal= {arXiv preprint arXiv:1209.3378},
year = {2014}
}
Comments
v2: minor corrections v3: reorganization, stronger rigidity statements