Sharp lower bounds for the asymptotic entropy of symmetric random walks
Sébastien GouëzelUniversité de Rennes, France
Frédéric MathéusUniversité de Bretagne-Sud, Vannes, France
François MaucourantUniversité de Rennes I, France
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.
Cite this article
Sébastien Gouëzel, Frédéric Mathéus, François Maucourant, Sharp lower bounds for the asymptotic entropy of symmetric random walks. Groups Geom. Dyn. 9 (2015), no. 3, pp. 711–735DOI 10.4171/GGD/325