Ergodicity of group actions and spectral gap, applications to random walks and Markov shifts

Jean-Pierre Conze, Yves Guivarc'h

Let $(X,\mathcal{B},\nu )$ be a probability space and let $\Gamma$ be a countable group of $\nu$-preserving invertible maps of $X$ into itself. To a probability measure $\mu$ on $\Gamma$ corresponds a…