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arXiv · 1205.5126

Group Extended Markov Systems, Amenability, and the Perron-Frobenius Operator

Johannes Jaerisch
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Abstract

We characterise amenability of a countable group in terms of the spectral radius of the Perron-Frobenius operator associated to a group extension of a countable Markov shift and a H\"older continuous potential. This extends a result of Day for random walks and recent work of Stadlbauer for dynamical systems. Moreover, we show that, if the potential satisfies a symmetry condition with respect to the group extension, then the logarithm of the spectral radius of the Perron-Frobenius operator is given by the Gurevic pressure of the potential.

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BibTeXRIS

Johannes Jaerisch. 2012-05-23. Group Extended Markov Systems, Amenability, and the Perron-Frobenius Operator. https://arxiv.org/abs/1205.5126

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