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Can extra updates delay mixing?

Tuesday 25th March 2008 - 11:40 to 12:30
INI Seminar Room 1

We consider Glauber dynamics (starting from an extremal configuration) in a monotone spin system, and show that interjecting extra updates cannot increase the expected Hamming distance and the total variation distance to the stationary distribution. We deduce that for monotone Markov random fields, when block dynamics contracts a weighted Hamming metric, so does single-site dynamics started at extremal configurations. In particular, our result completes work of Kenyon, Mossel and Peres concerning Glauber dynamics for the Ising model on trees. Our approach also shows that on bipartite $n$-vertex graphs, alternating updates systematically between odd and even vertices cannot improve the mixing time by more than a factor of $\log n$ compared to updates at uniform random locations. (Joint work with Peter Winkler).

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons