On the variational problem for upper tails in sparse random graphs

What is the probability that the number of triangles in Gn,p, the Erdős‐Rényi random graph with edge density p, is at least twice its mean? Writing it as exp[−r(n,p)], already the order of the rate function r(n, p) was a longstanding open problem when p = o(1), finally settled in 2012 by Chatterjee...

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Bibliographic Details

Published in:	Random structures & algorithms Vol. 50; no. 3; pp. 420 - 436
Main Authors:	Lubetzky, Eyal, Zhao, Yufei
Format:	Journal Article
Language:	English
Published:	Hoboken Wiley Subscription Services, Inc 01.05.2017
Subjects:	Asymptotic properties Constraining Density Deviation Graph theory Graphs large deviations sparse random graphs Triangles upper tails of subgraph counts Vibration
ISSN:	1042-9832, 1098-2418
Online Access:	Get full text
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