An entropy approach to the hard-core model on bipartite graphs (Q2731583)
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scientific article; zbMATH DE number 1626153
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An entropy approach to the hard-core model on bipartite graphs |
scientific article; zbMATH DE number 1626153 |
Statements
9 May 2002
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random independent sets
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entropy bounds
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phase transition
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An entropy approach to the hard-core model on bipartite graphs (English)
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Each independent set \(I\) of a fixed finite regular bipartite graph is assigned a probability that is proportional to a fixed positive parameter raised to the size of \(I\). An upper bound is given to the entropy of such probability distributions on the class of independent sets. Asymptotic results are given for the size of a random independent set. The entropy of the uniform distribution obtained with the parameter set to 1 leads to a sharp upper bound for the number of independent sets.
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