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Edge isoperimetry and rapid mixing on matroids and geometric Markov chains

Jung-Bae Son LFCS 4pm Tuesday 28 August 2001 Room 2511, JCMB, King's Buildings

We show how to bound the mixing time and log-Sobolev constants of Markov chains by bounding the edge-isoperimetry of their underlying graphs. To do this we use two recent techniques, one involving Average Conductance and the other log-Sobolev constants. We show a sort of strong conductance bound on a family of geometric Markov chains, give improved bounds for the mixing time of a Markov chain on balanced matroids, and in both cases

(Joint work with Ravi Montenegro.)

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