Radon stationary measures for a random walk on mathbbT^d \×\n \ℝ

2020/06/10 by Timothée Bénard, Bénard, Timothée
Mathematics · #Stochastic processes and statistical mechanics #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2006.05742

Abstract

We classify Radon stationary measures for a random walk on mathbbT^d\n\× \ℝ. This walk is realised by a random action of\nSL_d(\ℤ) on the mathbbT^d component, coupled with a\ntranslation on the \ℝ component. We show, under assumptions of\nirreducibility and recurrence, the rigidity and homogeneity of Radon ergodic\nstationary measures.\n

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