Fix an irrational number $\alpha$ and a smooth, positive, real function $p$
on the circle. If current position is $x$ then in the next step jump to
$x+\alpha$ with probability
$p(x)$ or to $x-\alpha$ with probability $1-p(x)$. In 1999 Sinai has proven
that if $p$ is asymmetric (in certain sense) or $\alpha$ is Diophantine
then this Markov process possesses a unique stationary distribution.
During the talk I will present the uniqueness of stationary distribution
in the case when $\alpha$ is arbitrary irrational and $p$ is symmetric.
This answers a recent question posed by D. Dolgopyat, B. Fayad and M. Saprykina.
Meeting ID: 852 4277 3200
Passcode: 103121