The random k cycle walk on the symmetric group

被引：6

作者：

Hough, Bob ^{[1
]}

机构：

[1] Stanford Univ, Dept Math, 450 Serra Mall, Stanford, CA 94305 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2016年 / 165卷 / 1-2期

基金：

欧洲研究理事会;

关键词：

Random walk on a group; Character bounds; Symmetric group; Cut-off phenomenon; FINITE-GROUPS; CHARACTERS; BOUNDS;

D O I：

10.1007/s00440-015-0636-6

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study the random walk on the symmetric group generated by the conjugacy class of cycles of length k. We show that the convergence to uniform measure of this walk has a cut-off in total variation distance after steps, uniformly in as . The analysis follows from a new asymptotic estimation of the characters of the symmetric group evaluated at cycles.

引用

页码：447 / 482

页数：36

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