Disjoint Decomposition of Markov Chains and Sampling Circuits in Cayley Graphs
Combinatorics, Probability and Computing
Blocking Conductance and Mixing in Random Walks
Combinatorics, Probability and Computing
Mathematical aspects of mixing times in Markov chains
Foundations and Trends® in Theoretical Computer Science
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We compute tight lower bounds on the log-Sobolev constant of a class of inductively defined Markov chains, which contains the bases 驴 exchange walks for balanced matroidsstudied by Feder and Mihail. As a corollary, we obtain improved upper bounds for the mixing time of a variety of Markov chains. An example: the "natural" random walk on spanning trees of a graph G as proposed by Broder 驴 which has been studied by a number of authors 驴 mixes in time O(mn log n),wheren is the number of vertices of G and m the number of edges. This beats the best previous upper bound on this walk by a factor n2.