ACTA issues

The time evolution of permutations under random stirring

Bálint Vető

Acta Sci. Math. (Szeged) 72:3-4(2006), 891-906

Abstract. We consider permutations of $\{1,\ldots,n\} $ obtained by $\lfloor\sqrt nt\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 $t\ge0$, as $n\to\infty $.

AMS Subject Classification (1991): 60C05

Received July 1, 2005, and in final form May 8, 2006. (Registered under 5948/2009.)