Sharp lower bounds for the asymptotic entropy of symmetric random walks

Sébastien Gouëzel; Frédéric Mathéus; François Maucourant

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arXiv · 1209.3378

Sharp lower bounds for the asymptotic entropy of symmetric random walks

Sébastien Gouëzel·Frédéric Mathéus·François Maucourant

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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.

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Sébastien Gouëzel, Frédéric Mathéus, François Maucourant. 2012-09-15. Sharp lower bounds for the asymptotic entropy of symmetric random walks. https://arxiv.org/abs/1209.3378

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