Inventiones mathematicae

, Volume 187, Issue 1, pp 37–59

Random walks on finite volume homogeneous spaces


DOI: 10.1007/s00222-011-0328-5

Cite this article as:
Benoist, Y. & Quint, JF. Invent. math. (2012) 187: 37. doi:10.1007/s00222-011-0328-5


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.

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.CNRS-Université Paris-SudOrsayFrance
  2. 2.CNRS-Université Paris-NordVilletaneuseFrance