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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.

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Authors and Affiliations

  1. CNRS-Université Paris-Sud, Orsay, France

    Yves Benoist

  2. CNRS-Université Paris-Nord, Villetaneuse, France

    Jean-Francois Quint

Authors
  1. Yves Benoist
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  2. Jean-Francois Quint
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Correspondence to Jean-Francois Quint.

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Benoist, Y., Quint, JF. Random walks on finite volume homogeneous spaces. Invent. math. 187, 37–59 (2012). https://doi.org/10.1007/s00222-011-0328-5

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  • DOI: https://doi.org/10.1007/s00222-011-0328-5

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