Vol. 14, No. 8, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 12, 2133–2308
Issue 11, 1945–2131
Issue 10, 1767–1943
Issue 9, 1589–1766
Issue 8, 1403–1587
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
Most words are geometrically almost uniform

Michael Jeffrey Larsen

Vol. 14 (2020), No. 8, 2185–2196
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.

Keywords
word maps, random walks on finite simple groups, groups of Lie type
Mathematical Subject Classification 2010
Primary: 20P05
Secondary: 11G25, 14G15, 20G40
Milestones
Received: 16 October 2019
Revised: 17 February 2020
Accepted: 25 March 2020
Published: 18 September 2020
Authors
Michael Jeffrey Larsen
Department of Mathematics
Indiana University
Rawles Hall
Bloomington, IN
United States