Random walks on finite volume homogeneous spaces
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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.
KeywordsRandom Walk Parabolic Subgroup Borel Probability Measure Unipotent Radical Zariski Closure
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