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arXiv · 1908.07287

Most Words are Geometrically Almost Uniform

Michael Larsen
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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| goes to infinity. In this paper, we show that the proportion is in fact 1.

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Michael Larsen. 2019-08-20. Most Words are Geometrically Almost Uniform. https://doi.org/10.2140/ant.2020.14.2185

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