Spectral gap for the interchange process in a box

Details Spectral gap for the interchange process in a box Spectral gap for the interchange process in a box

2008-05-05

arxiv.org/abs/0805.0480v1

Mathematics

Probability

8 pages. I learned after completing a draft of this paper that its main result had recently been obtained by Starr and Conomos

Scientific paper

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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