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On the ergodicity of difference distribution tables of random permutations

A. S. Maslov

Belarusian State University

Abstract: Properties of the Markov chain induced by the difference distribution table of a random permutation acting on a finite group $G$ are considered. The ergodicity probability and the convergence rate of this Markov chain are estimated. It is proved that the group generated by permutations $x\mapsto s(xa)$, $x,a\in G$, is $2$-transitive for almost all permutations $s$ from the permutation group of $G$.

UDC: 519.214.7+512.542.74

Received: 17.11.2005