An Entropy Approach to the Hard-Core Model on Bipartite Graphs

Authors:
Jeff Kahn
Affiliations:
Department of Mathematics and RUTCOR, Rutgers University, New Brunswick, NJ 08903, USA (e-mail: jkahn@math.rutgers.edu)
Venue:
Combinatorics, Probability and Computing
Year:
2001

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Abstract

We use entropy ideas to study hard-core distributions on the independent sets of a finite, regular bipartite graph, specifically distributions according to which each independent set I is chosen with probability proportional to λ∣I∣ for some fixed λ 0. Among the results obtained are rather precise bounds on occupation probabilities; a ‘phase transition’ statement for Hamming cubes; and an exact upper bound on the number of independent sets in an n-regular bipartite graph on a given number of vertices.