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2008 Spectral gap for the interchange process in a box
Ben Morris
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Electron. Commun. Probab. 13: 311-318 (2008). DOI: 10.1214/ECP.v13-1381

Abstract

We show that the spectral gap for the interchange process (and the symmetric exclusion process) in a $d$-dimensional box of side length $L$ is asymptotic to $\pi^2/L^2$. This gives more evidence in favor of Aldous's conjecture that in any graph the spectral gap for the interchange process is the same as the spectral gap for a corresponding continuous-time random walk. Our proof uses a technique that is similar to that used by Handjani and Jungreis, who proved that Aldous's conjecture holds when the graph is a tree.

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Ben Morris. "Spectral gap for the interchange process in a box." Electron. Commun. Probab. 13 311 - 318, 2008. https://doi.org/10.1214/ECP.v13-1381

Information

Accepted: 17 June 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60180
MathSciNet: MR2415139
Digital Object Identifier: 10.1214/ECP.v13-1381

Subjects:
Primary: 60J25

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