Sharp Estimates for the Entropy

François Ledrappier
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François Ledrappier: Université de Paris VI, Laboratoire de Probabilités, T. 56

A chapter in Harmonic Analysis and Discrete Potential Theory, 1992, pp 281-288 from Springer

Abstract: Abstract In this paper, we consider three different exponential rates of growth associated to a symmetric random walk on a countable group: the spectral gap, the entropy and the decay of the fundamental state along the paths of the random walk. We prove general inequalities between these numbers. We hope that these inequalities, and the characterization of the cases of equality, would enable us to express fine properties of the group through rather coarse invariants.

Keywords: Markov Operator; Galois Cover; Symmetric Random Walk; Harmonic Manifold; Entropy Profile (search for similar items in EconPapers)
Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-2323-3_23

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DOI: 10.1007/978-1-4899-2323-3_23

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