Words and mixing times in finite simple groups

Gili Schul; Aner Shalev

Words and mixing times in finite simple groups

Gili Schul, Aner Shalev

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

Let w ≠ 1 be a non-trivial group word, let G be a finite simple group, and let w.G/be the set of values of w in G. We show that if G is large, then the random walk on G with respect to w.G/ as a generating set has mixing time 2. This strengthens various known results, for example the fact that w(G) ² covers almost all of G.

Original language	English
Pages (from-to)	517-535
Number of pages	19
Journal	Groups, Geometry, and Dynamics
Volume	5
Issue number	2
State	Published - 2011

Keywords

Finite simple groups
Mixing time
Random walks
Words

All Science Journal Classification (ASJC) codes

Geometry and Topology
Discrete Mathematics and Combinatorics

Cite this

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title = "Words and mixing times in finite simple groups",

abstract = "Let w ≠ 1 be a non-trivial group word, let G be a finite simple group, and let w.G/be the set of values of w in G. We show that if G is large, then the random walk on G with respect to w.G/ as a generating set has mixing time 2. This strengthens various known results, for example the fact that w(G) 2 covers almost all of G.",

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AB - Let w ≠ 1 be a non-trivial group word, let G be a finite simple group, and let w.G/be the set of values of w in G. We show that if G is large, then the random walk on G with respect to w.G/ as a generating set has mixing time 2. This strengthens various known results, for example the fact that w(G) 2 covers almost all of G.

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KW - Mixing time

KW - Random walks

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M3 - مقالة

SN - 1661-7207

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EP - 535

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

IS - 2

ER -

Words and mixing times in finite simple groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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Cite this