Behaviors of entropy on finitely generated groups
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Jérémie Brieussel [1]
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[1] Kyoto University
Kyoto University
Kamigyō-ku, Japón
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- Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 6, 2013, págs. 4116-4161
- Idioma: inglés
- DOI: 10.1214/12-AOP761
- Texto completo no disponible (Saber más ...)
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Resumen
A variety of behaviors of entropy functions of random walks on finitely generated groups is presented, showing that for any 12≤α≤β≤1, there is a group Γ with measure μ equidistributed on a finite generating set such that lim inflogHΓ,μ(n)logn=α,lim suplogHΓ,μ(n)logn=β.
The groups involved are finitely generated subgroups of the group of automorphisms of an extended rooted tree. The return probability and the drift of a simple random walk Yn on such groups are also evaluated, providing an example of group with return probability satisfying lim inflog|logP(Yn=Γ1)|logn=13,lim suplog|logP(Yn=Γ1)|logn=1 and drift satisfying lim inflogE∥Yn∥logn=12,lim suplogE∥Yn∥logn=1.
