Date
Mon, 12 Nov 2007
Time
14:45 - 15:45
Location
Oxford-Man Institute
Speaker
Professor Mark Jerrum
Organisation
Queen Mary University, London

Joint work with Martin Dyer (Leeds) and Leslie Goldberg (Liverpool).

A spin system may be modelled as a graph, in which edges (bonds) indicate interactions between adjacent vertices (sites). A configuration of the system is an assignment of colours (spins) to the vertices of the graph. The interactions between adjacent spins define a certain distribution, the Boltzmann distribution, on configurations. To sample from this distribution it is usually necessary to simulate one of a number of Markov chains on the space of all configurations. Theoretical analyses of the mixing time of these Markov chains usually assume that spins are updated at single vertices chosen uniformly at random. Actual simulations, in contrast, may make (random) updates according to a deterministic, usually highly structured pattern. We'll explore the relationships between systematic scan and random single-site updates, and also between classical uniqueness conditions from statistical physics and more recent techniques in mixing time analysis.

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