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.
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