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Abstract
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 ErdosRenyi graphs near criticality.
Original language  English 

Pages (fromto)  19892021 
Number of pages  33 
Journal  Annals of Applied Probability 
Volume  20 
Issue number  6 
DOIs  
Publication status  Published  Dec 2010 
Keywords
 random graph
 degree distribution
 typed graph
 entropy
 partition function
 random randomly colored graph
 relative entropy
 spins
 Ising model on a random graph
 ErdosRenyi graph
 joint large deviation principle
 empirical pair measure
 empirical measure
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Projects
 1 Finished

INTERSECTION LOCAL TIMES AND STOCHASTIC PROCESSES IN RANDOM MEDIA
Morters, P.
Engineering and Physical Sciences Research Council
1/09/05 → 31/08/10
Project: Research council