Geodesic
On the ergodicity of difference distribution tables of random permutations
Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 86-94

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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 $G$. 
@article{TIMB_2006_14_2_a10,
     author = {A. S. Maslov},
     title = {On the ergodicity of difference distribution tables of random permutations},
     journal = {Trudy Instituta matematiki},
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     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2006_14_2_a10/}
}
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A. S. Maslov. On the ergodicity of difference distribution tables of random permutations. Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 86-94. http://geodesic.mathdoc.fr/item/TIMB_2006_14_2_a10/