Stein's method, semicircle distribution, and reduced decompositions of the longest element in the symmetric group

Jason Fulman; Larry Goldstein

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arXiv · 1405.1088

Stein's method, semicircle distribution, and reduced decompositions of the longest element in the symmetric group

Jason Fulman·Larry Goldstein

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Abstract

Consider a uniformly chosen random reduced decomposition of the longest element in the symmetric group. It is known that the location of the first transposition in this decomposition converges to the semicircle distribution. In this note we provide a sharp error term for this result, using the "comparison of generators" approach to Stein's method.

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Jason Fulman, Larry Goldstein. 2014-05-05. Stein's method, semicircle distribution, and reduced decompositions of the longest element in the symmetric group. https://arxiv.org/abs/1405.1088

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