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Please use this identifier to cite or link to this item: http://repositorio.ufba.br/ri/handle/ri/12030

Title: An extension of Kesten’s criterion for amenability to topological Markov chains
Other Titles: Advances in Mathematics
Authors: Stadlbauer, Manuel
Keywords: Amenability;Group extension;Topological Markov chain;Thermodynamic formalism;Periodic manifold
Issue Date: 2013
Publisher: Advances in Mathematics
Abstract: The main results of this note extend a theorem of Kesten for symmetric random walks on discrete groups to group extensions of topological Markov chains. In contrast to the result in probability theory, there is a notable asymmetry in the assumptions on the base. That is, it turns out that, under very mild assumptions on the continuity and symmetry of the associated potential, amenability of the group implies that the Gurevič-pressures of the extension and the base coincide whereas the converse holds true if the potential is Hölder continuous and the topological Markov chain has big images and preimages. Finally, an application to periodic hyperbolic manifolds is given
Description: Texto completo. Acesso restrito. p. 450–468
URI: http://www.repositorio.ufba.br/ri/handle/ri/12030
ISSN: 0001-8708
Appears in Collections:Artigos Publicados em Periódicos (IM)

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