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arXiv · 1109.3915

A Coupling Argument for the Random Transposition Walk

Olena Bormashenko
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Abstract

This paper explores the mixing time of the random transposition walk on the symmetric group. While it has long been known that this walk mixes in order n*log(n) time, this result has not previously been attained using coupling. A coupling argument showing the correct order mixing time is presented. This is accomplished by first projecting to conjugacy classes, and then using the Bubley-Dyer path coupling construction. In order to obtain appropriate bounds on the time it takes the path coupling to meet, ideas from Schramm's paper "Compositions of Random Transpositions" are used.

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Olena Bormashenko. 2011-09-18. A Coupling Argument for the Random Transposition Walk. https://arxiv.org/abs/1109.3915

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