Bounding Fastest Mixing
Sébastien Roch, University of California at Berkeley, USA
Abstract
In a recent work,
Boyd, Diaconis and Xiao
introduced a semidefinite programming approach
for computing
the fastest mixing Markov chain on a graph of allowed transitions,
given a target stationary distribution. In this paper, we show that
standard mixing time analysis techniques---variational
characterizations, conductance, canonical paths---can
be used to give simple, nontrivial lower and upper bounds
on the fastest mixing time. To test the applicability of this idea,
we consider several detailed examples including
the Glauber dynamics of the Ising model.
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