[Papers]
[Alex Furman]

Stationary measures and equidistribution for orbits of nonabelian semigroups
on the torus

Let *p* be a probability measure on SL_{d}(**Z**) satisfying certain the moment condition.
We show that if the group generated by the support of *p* is large enough, in particular if this group is Zariski dense in SL_{d}(**R**),
then the random walk on the torus starting at any irrational
point tends to the uniform measure on the torus.
If the initial point is Diophantine generic, we show this convergence is exponentially fast.

Authors:
J. Bourgain,
A. Furman,
E. Lindenstrauss,
S. Mozes

Bibliographical: J. Amer. Math. Soc. **24** (2011), pp. 231--280.

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[Papers]
[Alex Furman]