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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Large Deviation Principle for the Erds-Renyi random graph

## Large Deviation Principle for the Erds-Renyi random graphAdd to your list(s) Download to your calendar using vCal - Chatterjee, S (Courant Institute)
- Friday 01 April 2011, 14:00-15:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Discrete Analysis What does an Erdos-Renyi graph look like when a rare event happens? I will describe an answer to 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. This is based on joint work with S. R. S. Varadhan. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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