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Article overview
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Unique ergodicity of simple symmetric random walks on the circle | Klaudiusz Czudek
; | Date: |
4 Jan 2023 | Abstract: | Fix an irrational number $alpha$ and a smooth, positive, real function
$mathfrak{p}$ on the circle. If current position is $xin mathbb R/mathbb Z$
then in the next step jump to $x+alpha$ with probability $mathfrak{p}(x)$ or
to $x-alpha$ with probability $1-mathfrak{p}(x)$. In 1999 Sinai has proven
that if $mathfrak{p}$ is asymmetric (in certain sense) or $alpha$ is
Diophantine then the Markov process possesses a unique stationary distribution.
Next year Conze and Guivarc’h showed the uniqueness of stationary distribution
for an arbitrary irrational angle $alpha$. In this note we present a new proof
of latter result. | Source: | arXiv, 2301.01496 | Services: | Forum | Review | PDF | Favorites |
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