Advances in Mathematics
| Autor: | Manuel Stadlbauer |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Mathematics(all)
General Mathematics Hölder condition Dynamical Systems (math.DS) Topological Markov chain Topology 01 natural sciences Periodic manifold Probability theory Amenability FOS: Mathematics 0101 mathematics Mathematics - Dynamical Systems Group extension Mathematics Discrete mathematics 37A50 37C30 20F69 Markov chain Group (mathematics) Probability (math.PR) 010102 general mathematics Base (topology) Random walk 010101 applied mathematics Thermodynamic formalism Symmetry (geometry) Mathematics - Probability |
| Zdroj: | Repositório Institucional da UFBA Universidade Federal da Bahia (UFBA) instacron:UFBA |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2012.12.004 |
| Popis: | 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 Gurevic-pressures of the extension and the base coincide whereas the converse holds true if the potential is H\"older continuous and the topological Markov chain has big images and preimages. Finally, an application to periodic hyperbolic manifolds is given. Comment: New proof of Lemma 5.3 due to the gap in the first version of the article |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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