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March 2016 Mixing time and cutoff for the adjacent transposition shuffle and the simple exclusion
Hubert Lacoin
Ann. Probab. 44(2): 1426-1487 (March 2016). DOI: 10.1214/15-AOP1004

Abstract

In this paper, we investigate the mixing time of the adjacent transposition shuffle for a deck of $N$ cards. We prove that around time $N^{2}\log N/(2\pi^{2})$, the total variation distance to equilibrium of the deck distribution drops abruptly from $1$ to $0$, and that the separation distance has a similar behavior but with a transition occurring at time $(N^{2}\log N)/\pi^{2}$. This solves a conjecture formulated by David Wilson. We present also similar results for the exclusion process on a segment of length $N$ with $k$ particles.

Citation

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Hubert Lacoin. "Mixing time and cutoff for the adjacent transposition shuffle and the simple exclusion." Ann. Probab. 44 (2) 1426 - 1487, March 2016. https://doi.org/10.1214/15-AOP1004

Information

Received: 1 January 2014; Revised: 1 January 2015; Published: March 2016
First available in Project Euclid: 14 March 2016

zbMATH: 06579694
MathSciNet: MR3474475
Digital Object Identifier: 10.1214/15-AOP1004

Subjects:
Primary: 37L60, 60J10, 82C20

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 2 • March 2016
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