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Klaudiusz Czudek: Simple symmetric random walks on the circle

Time: Thu 2022-10-20 13.00


Participating: Klaudiusz Czudek (Nicolas Copernicus University in Toruń, Poland)

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Abstract: 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 $1-p(x)$. Throughout the talk I will recall results of Sinai and Conze-Guivarc'h concerning uniqueness of stationary distribution for this random walk and discuss its mixing properties.