## Speaker:

Associate Professor Vadim Kaloshin

## Institution:

Cal Tech

## Time:

Tuesday, May 17, 2005 - 11:00am

## Location:

MSTB 254

Consider a compact manifold $M$ (e.g. a torus) equipped with

a smooth measure $\mu$ (e.g. Lebesgue measure in the case

of torus) as a probability space $(M,\mathcal M,\mu)$. Consider

an ergodic map $T:M \to M$ along with a smooth function

$p:M \to (0,1)$. Define a random walk along orbits of $T$ as follows:

a point $x$ jumps to $T x$ with probability $p(x)$ and

to $T^{-1} x$ with probability $1-p(x)$.

Is there a limiting distribution of such a random walk for a generic

initial point? Is it absolutely continuous with respect to $\mu$?

We shall present an answer for several essentially different

maps $T$.