Sharp lower bounds for the asymptotic entropy of symmetric random walks | Zendy

Sébastien Gouëzel | Zendy; Frédéric Mathéus | Zendy; François Maucourant | Zendy

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Sharp lower bounds for the asymptotic entropy of symmetric random walks

Author(s) -

Sébastien Gouëzel,

Frédéric Mathéus,

François Maucourant

Publication year - 2015

Publication title -

groups geometry and dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.05

H-Index - 25

eISSN - 1661-7215

pISSN - 1661-7207

DOI - 10.4171/ggd/325

Subject(s) - mathematics , random walk , countable set , spectral radius , entropy (arrow of time) , inequality , upper and lower bounds , combinatorics , statistical physics , pure mathematics , mathematical analysis , statistics , eigenvalues and eigenvectors , physics , quantum mechanics

v2: minor corrections v3: reorganization, stronger rigidity statementsInternational audienceThe 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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