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Non-proximal linear random walks on the torus

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Given a a probability measure µ on SL(d,Z), the associated random walk on the linear group induces a random walk on the d-dimensional torus Rd/Zd. Bourgain-Furman-Lindenstrauss-Mozes showed that the random walk equidistributes to the Haar measure provided that the starting point is irrational, µ has finite exponential moment and that the group generated by the support of µ acts irreducibly and proximally on R^d. In this talk, I will explain how to get the same result for certain non-proximal groups (for example SL(d,C)) using their method combined with new tools from additive combinatorics.

This talk is part of the Discrete Analysis Seminar series.

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