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

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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.

Original languageEnglish (US)
Pages (from-to)219-237
Number of pages19
JournalCombinatorics Probability and Computing
Volume10
Issue number3
DOIs
StatePublished - Dec 1 2001

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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