The large deviation principle for the Erdo{double acute}s-Rényi random graph

Sourav Chatterjee, S. R.S. Varadhan

Research output: Contribution to journalArticle

Abstract

What does an Erdo{double acute}s-Rényi graph look like when a rare event happens? This paper answers this question when p is fixed and n tends to infinity by establishing a large deviation principle under an appropriate topology. The formulation and proof of the main result uses the recent development of the theory of graph limits by Lovász and coauthors and Szemerédi's regularity lemma from graph theory. As a basic application of the general principle, we work out large deviations for the number of triangles in G(n,p). Surprisingly, even this simple example yields an interesting double phase transition.

Original languageEnglish (US)
Pages (from-to)1000-1017
Number of pages18
JournalEuropean Journal of Combinatorics
Volume32
Issue number7
DOIs
StatePublished - Oct 1 2011

    Fingerprint

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this