Large deviation principles for empirical measures of colored random graphs
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Date
2010
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Journal ISSN
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Publisher
Annals of Applied Probability 6(20): 1989-2021
Abstract
For any finite colored graph we define the empirical neighborhood
measures, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number of edges connecting each pair of colors. For a class of models of sparse colored random graphs, we prove large deviation principles for these empirical measures In the weak topology. The rate functions governing our large deviation principles can be expressed explicitly in terms of relative entropies. We derive a large deviation principle for the degrees distribution of ErÖÖs-Réenyl graphs near criticality.
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Keywords
Random graph, Erdős–Rényi graph, random randomly colored graph, typed graph, spins, joint large deviation principle, empirical pair measure, empirical measure, degree distribution, entropy, relative entropy, Ising model on a random graph, partition function