# Random walks with bounded first moment on finite-volume spaces

@inproceedings{Benard2021RandomWW, title={Random walks with bounded first moment on finite-volume spaces}, author={Timoth'ee B'enard and Nicolas de Saxc'e}, year={2021} }

Let G be a real Lie group, Λ ≤ G a lattice, and Ω = G/Λ. We study the equidistribution properties of the left random walk on Ω induced by a probability measure μ on G. It is assumed that μ has a finite first moment, and that the Zariski closure of the group generated by the support of μ in the adjoint representation is semisimple without compact factors. We show that for every starting point x ∈ Ω, the μ-walk with origin x has no escape of mass, and equidistributes in Cesàro averages toward…

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