%0 Journal Article
%T Group Extended Markov Systems, Amenability, and the Perron-Frobenius Operator
%A Johannes Jaerisch
%J Mathematics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1205.5126v4