On the joint behaviour of speed and entropy of random walks on groups

Gideon Amir

doi:10.4171/ggd/403

On the joint behaviour of speed and entropy of random walks on groups

Gideon Amir

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

For every 3=4 ; < 1 satisfying 1C 2 we construct a finitely generated group and a (symmetric, finitely supported) random walk Xn on so that its expected distance from its starting point satisfies EjXnj n and its entropy satisfies H.Xn/ n. In fact, the speed and entropy can be set precisely to equal any two nice enough prescribed functions f; h up to a constant factor as long as the functions satisfy the relation for some.

Original language	English
Pages (from-to)	455-467
Number of pages	13
Journal	Groups, Geometry, and Dynamics
Volume	11
Issue number	2
DOIs	https://doi.org/10.4171/ggd/403
State	Published - 2017

Keywords

Automaton groups.d
Entropy
Groups
Permutation wreath product
Random walk
Rate of escape

All Science Journal Classification (ASJC) codes

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.4171/ggd/403

Cite this

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On the joint behaviour of speed and entropy of random walks on groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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