Tight upper tail bounds for cliques

Authors:
B. Demarco;J. Kahn
Affiliations:
Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854;Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854
Venue:
Random Structures & Algorithms
Year:
2012

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Abstract

With ξk =ξ **math-image** the number of copies of Kk in the usual (Erdős-Rényi) random graph G(n,p), p ≥ n-2/(k-1) and η 0, we show when k 1 \documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath}\pagestyle{empty}\begin{document}\begin{align*} \Pr(\xi_k (1+\eta)[\textbf[ E]] \xi_k)