Sharp lower bounds for the asymptotic entropy of symmetric random walks
Résumé
The entropy, the spectral radius and the drift are important numerical quantities associated to any random walk with finite second moment on a countable group. We prove an optimal inequality relating those quantities, 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.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)