1/13/2004 The Ising model on trees: Boundary conditions and mixing time joint work with Martinelli & Sinclair; Dror Weitz  -   University of California, Berkeley

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You are invited to attend...

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WHO: Dror Weitz

AFFILIATION: University of California at Berkeley

TITLE: The Ising model on trees:

Boundary conditions and mixing time joint work with Fabio Martinelli and Alistair Sinclair

WHEN: Tue 1/13/2004

WHERE: 113/1021 Research Lecture Room, Microsoft Research

TIME: 10:30AM-12:00PM

HOST: Christian Borgs

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ABSTRACT:

We give the first comprehensive analysis of the effect of boundary conditions on the mixing time of the Glauber dynamics for the Ising model. Specifically, we show that the mixing time on an $n$-vertex regular tree with plus-boundary remains $O(n\log n)$ at all temperatures (in contrast to the free boundary case, where the mixing time is not bounded by any fixed polynomial at low temperatures). We also show that this bound continues to hold in the presence of an arbitrary external field. Our results are actually stronger, and provide tight bounds on the log-Sobolev constant and the spectral gap of the dynamics. In addition, our methods yield simpler proofs and stronger results for the mixing time in the regime where it is insensitive to the boundary conditions. Our techniques also apply to a much wider class of models, including those with hard-core constraints like the antiferromagnetic Potts model at zero temperature (proper colorings) and the hard-core lattice gas (independent sets).

BIO:

Dror Weitz is a Ph.D. candidate (will graduate in May 2004) in the Computer Science Division at the University of California, Berkeley. He received his B.Sc. in Computer Science and Economics from the Hebrew University of Jerusalem, Israel. His current research focuses on relationships between temporal and spatial notions of phase transitions in statistical physics. He is also interested in intersections of applied probability and algorithms with other scientific fields such as the socio-economic sciences

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