The large deviation principle for the Erdős-Rényi random graph

Details The large deviation principle for the Erdős-Rényi random graph The large deviation principle for the Erdős-Rényi random graph

2010-08-11

arxiv.org/abs/1008.1946v3

Mathematics

Probability

24 pages. To appear in European J. Comb. (special issue on graph limits)

Scientific paper

What does an Erdos-Renyi 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 Lovasz and coauthors and Szemeredi'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.

Affiliated with

Also associated with

No associations

Rating

The large deviation principle for the Erdős-Rényi random graph does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The large deviation principle for the Erdős-Rényi random graph, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The large deviation principle for the Erdős-Rényi random graph will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-480461