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Anirban Basak (Weizmann Institute of Science, Israel)

Wed, 11 October 2017, 11:00 to 12:00

Emmy Noether Seminar Room, ICTS Campus, Bangalore

Abstract

The study of statistical physics models on sparse graphs is motivated by numerous examples in combinatorics, computer science, and statistical inference. The Ising model is a paradigm model in statistical physics. It is believed that for a wide class of large graphs the Ising measure decomposes into a convex combination of well-separated simple components. Loosely speaking, in locally tree-like graphs the neighborhood of a typical vertex has approximately the law of the neighborhood of the root of a randomly chosen limiting tree. In the context of locally tree-like graphs, the decomposition of the Ising measure was previously proven only for $k$-regular limit.

In this talk, I will describe that the Ising measure on a general sequence of locally tree-like graphs converges to the symmetric mixture of the plus and minus Ising measure on the limiting tree, yielding the universality of the above phenomenon. I will also illustrate that the Ising measure conditioned on the sum of spins being positive on locally tree-like expander graphs converges to the plus Ising measure on the limiting tree. These results unify to provide a thorough understanding of the Ising measure on locally tree-like graphs.

This is a joint work with Amir Dembo.