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The time evolution of permutations under random stirring

Bálint Vető
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Abstract

We consider permutations of $\{1,...,n\}$ obtained by $\lfloor\sqrt{n}t\rfloor$ independent applications of random stirring. In each step the same marked stirring element is transposed with probability $1/n$ with any one of the $n$ elements. Normalizing by $\sqrt{n}$ we describe the asymptotic distribution of the cycle structure of these permutations, for all $t\ge 0$, as $n\to\infty$.

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Bálint Vető. 2006-03-02. The time evolution of permutations under random stirring. https://arxiv.org/abs/math/0603044

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