Geodesic
Sharp lower bounds for the asymptotic entropy of symmetric random walks
Sébastien Gouëzel1 ; Frédéric Mathéus2 ; François Maucourant3
1Université de Rennes, France
2Université de Bretagne-Sud, Vannes, France
3Université de Rennes I, France
Groups, geometry, and dynamics, Tome 9 (2015) no. 3, pp. 711-735

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DOI

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.
DOI : 10.4171/ggd/325
Classification : 05-XX, 60-XX
Mots-clés : Random walk, countable group, entropy, spectral radius, drift, volume growth, Poisson boundary

Sébastien Gouëzel  1   ; Frédéric Mathéus  2   ; François Maucourant  3

1 Université de Rennes, France
2 Université de Bretagne-Sud, Vannes, France
3 Université de Rennes I, France 
Sébastien Gouëzel; Frédéric Mathéus; François Maucourant. Sharp lower bounds for the asymptotic entropy of symmetric random walks. Groups, geometry, and dynamics, Tome 9 (2015) no. 3, pp. 711-735. doi: 10.4171/ggd/325
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     title = {Sharp lower bounds for the asymptotic entropy of symmetric random walks},
     journal = {Groups, geometry, and dynamics},
     pages = {711--735},
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     doi = {10.4171/ggd/325},
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