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An introduction to the Mayer expansion

Presented by: 
A Sokal [NYU/UCL]
Monday 7th April 2008 - 11:30 to 12:30
INI Seminar Room 1

I define the repulsive lattice gas on a vertex set X (which includes the independent-set polynomial of a graph G as a special case) and briefly explain its relevance in statistical physics and in combinatorics. I then describe the Mayer expansion for the logarithm of the lattice-gas partition function, and analyze some of its combinatorial properties. Next, I describe two approaches to proving the convergence of the Mayer expansion in a complex polydisc: the traditional graphical approach and Dobrushin's inductive approach. Finally, I explain briefly the surprising connection between the independent-set polynomial and the Lovasz local lemma in probabilistic combinatorics.

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