Random walks and rank one isometries on CAT(0) spaces

2022/05/16 by Bars, Corentin Le
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2205.07594

Abstract

Let G be a discrete group, μ a measure on G and X a proper CAT(0) space. We show that if G acts non-elementarily with a rank one element on X, then the pushforward \Z_n o \_n to X of the random walk generated by μ converges almost surely to a rank one point of the boundary. We also show that in this context, there is a unique stationary measure on the visual boundary ∂_∞ X of X, and that the drift of the random walk is almost surely positive.

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