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2020 Most words are geometrically almost uniform
Michael Jeffrey Larsen
Algebra Number Theory 14(8): 2185-2196 (2020). DOI: 10.2140/ant.2020.14.2185

Abstract

If w is a word in d > 1 letters and G is a finite group, evaluation of w on a uniformly randomly chosen d -tuple in G gives a random variable with values in G , which may or may not be uniform. It is known that if G ranges over finite simple groups of given root system and characteristic, a positive proportion of words w give a distribution which approaches uniformity in the limit as | G | . In this paper, we show that the proportion is in fact 1 .

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Michael Jeffrey Larsen. "Most words are geometrically almost uniform." Algebra Number Theory 14 (8) 2185 - 2196, 2020. https://doi.org/10.2140/ant.2020.14.2185

Information

Received: 16 October 2019; Revised: 17 February 2020; Accepted: 25 March 2020; Published: 2020
First available in Project Euclid: 12 November 2020

MathSciNet: MR4172705
Digital Object Identifier: 10.2140/ant.2020.14.2185

Subjects:
Primary: 20P05
Secondary: 11G25 , 14G15 , 20G40

Keywords: groups of Lie type , random walks on finite simple groups , word maps

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 8 • 2020
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