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Stiffness for Random Walks on Locally symmetric spaces

Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015

May 15, 2015 (02:30 PM PDT - 03:20 PM PDT)
Speaker(s): Alex Eskin (University of Chicago)
Location: MSRI: Simons Auditorium
  • stationary measure

  • uniformly expanding measure

  • quotients of Lie groups

  • entropy

  • amenable groups

  • Ratner's Theorem

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



Let G be a semisimple Lie group, and \Gamma a lattice. in G. Let \mu be a measure on G. We show that under a certain condition on \mu, any \mu-stationary measure on G/\Gamma is in fact invariant under the group generated by the support of \mu. We give an alternative argument (which bypasses the Local Limit Theorem) for some of the breakthrough results of Benoist and Quint in this area. This is joint work with Elon Lindenstrauss

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