The missing log in large deviations for triangle counts

Authors:
Sourav Chatterjee
Affiliations:
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012
Venue:
Random Structures & Algorithms
Year:
2012

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Abstract

This paper solves the problem of sharp large deviation estimates for the upper tail of the number of triangles in an Erdős-Rényi random graph, by establishing a logarithmic factor in the exponent that was missing till now. It is possible that the method of proof may extend to general subgraph counts. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 437–451, 2012 © 2012 Wiley Periodicals, Inc.