Large deviation principles for empirical measures of colored random graphs

Details Large deviation principles for empirical measures of colored random graphs Large deviation principles for empirical measures of colored random graphs

2006-07-21

arxiv.org/abs/math/0607545v2

Annals of Applied Probability 2010, Vol. 20, No. 6, 1989-2021

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP647 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP647

For any finite colored graph we define the empirical neighborhood measure, 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 degree distribution of Erd\H{o}s--R\'{e}nyi graphs near criticality.

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