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Spectral gap for the interchange process in a box

   
@article{ECP1381,
	author = {Ben Morris},
	title = {Spectral gap for the interchange process in a box},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {13},
	year = {2008},
	keywords = {spectral gap, interchange process},
	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.},
	pages = {no. 31, 311-318},
	issn = {1083-589X},
	doi = {10.1214/ECP.v13-1381},    
        url = {http://ecp.ejpecp.org/article/view/1381}}