, Volume 187, Issue 1, pp 37-59
Date: 29 Mar 2011

Random walks on finite volume homogeneous spaces

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Abstract

Extending previous results by A. Eskin and G. Margulis, and answering their conjectures, we prove that a random walk on a finite volume homogeneous space is always recurrent as soon as the transition probability has finite exponential moments and its support generates a subgroup whose Zariski closure is semisimple.