Large deviation principles for empirical measures of coloured random graphs

Kwabena Doku-Amponsah, Peter Morters

Research output: Contribution to journalArticle

10 Citations (Scopus)

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 Erdos-Renyi graphs near criticality.
Original languageEnglish
Pages (from-to)1989-2021
Number of pages33
JournalAnnals of Applied Probability
Volume20
Issue number6
DOIs
Publication statusPublished - 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
  • Erdos-Renyi graph
  • joint large deviation principle
  • empirical pair measure
  • empirical measure

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