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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 31 open journal systems 


Spectral gap for the interchange process in a box

Ben Morris, UC Davis


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 π2/L2. 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.


Full text: PDF

Pages: 311-318

Published on: June 17, 2008
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Electronic Communications in Probability. ISSN: 1083-589X