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- W4378510291 abstract "Fix an irrational number $alpha$ and a smooth, positive function $mathfrak{p}$ on the circle. If a particle is placed at a point $xin mathbb R/mathbb Z$, then in the next step it jumps to $x+alpha$ with probability $mathfrak{p}(x)$ and to $x-alpha$ with probability $1-mathfrak{p}(x)$. Sinai proved that if $mathfrak{p}$ is asymmetric (in certain sense) or $mathfrak{p}$ is symmetric and $alpha$ is Diophantine then this random walk is mixing. Here we show it is mixing for every irrational frequency and generic symmetric absolutely continuous $mathfrak{p}$. This can be rephrased as mixing of environment viewed from a particle. This partially answers a question posed by Dolgopyat, Fayad and Saprykina in 2019." @default.
- W4378510291 created "2023-05-27" @default.
- W4378510291 creator A5045260110 @default.
- W4378510291 date "2023-05-23" @default.
- W4378510291 modified "2023-09-30" @default.
- W4378510291 title "Mixing of generic simple symmetric random walk on the circle" @default.
- W4378510291 doi "https://doi.org/10.48550/arxiv.2305.14559" @default.
- W4378510291 hasPublicationYear "2023" @default.
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