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

Published online by Cambridge University Press:  25 June 2001

JEFF KAHN
Affiliation:
Department of Mathematics and RUTCOR, Rutgers University, New Brunswick, NJ 08903, USA (e-mail: jkahn@math.rutgers.edu)

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[mid ]I[mid ] 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.

Type
Research Article
Copyright
2001 Cambridge University Press

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