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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Vydané v:	Random structures & algorithms Ročník 50; číslo 3; s. 420 - 436
Hlavní autori:	Lubetzky, Eyal, Zhao, Yufei
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Hoboken Wiley Subscription Services, Inc 01.05.2017
Predmet:	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
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