Radon stationary measures for a random walk on ${\mathbb{T}}^d\times \mathbb{R}$

Abstract

We classify Radon stationary measures for a random walk on ${\mathbb{T}}^d\times \mathbb{R}$. This walk is realised by a random action of $S{L}_d(\mathbb{Z})$ on the ${\mathbb{T}}^d$ component, coupled with a translation on the $\mathbb{R}$ component. We show, under assumptions of irreducibility and recurrence, the rigidity and homogeneity of Radon ergodic stationary measures.

arXiv commentThe article is written in French. It was published on HAL on 12 March 2020