Electronic Communications in Probability

Spectral gap for the interchange process in a box

Ben Morris

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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.

Article information

Electron. Commun. Probab. Volume 13 (2008), paper no. 31, 311-318.

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

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Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces

spectral gap interchange process

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Morris, Ben. Spectral gap for the interchange process in a box. Electron. Commun. Probab. 13 (2008), paper no. 31, 311--318. doi:10.1214/ECP.v13-1381. http://projecteuclid.org/euclid.ecp/1465233458.

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