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April 2011 Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs
Svante Janson, Andrzej Ruciński
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Ark. Mat. 49(1): 79-96 (April 2011). DOI: 10.1007/s11512-009-0117-1

Abstract

General upper tail estimates are given for counting edges in a random induced subhypergraph of a fixed hypergraph ℋ, with an easy proof by estimating the moments. As an application we consider the numbers of arithmetic progressions and Schur triples in random subsets of integers. In the second part of the paper we return to the subgraph counts in random graphs and provide upper tail estimates in the rooted case.

Funding Statement

A. Ruciński supported by Polish grant N201036 32/2546. Research was performed while the authors visited Institut Mittag-Leffler in Djursholm, Sweden, during the program Discrete Probability, 2009.

Citation

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Svante Janson. Andrzej Ruciński. "Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs." Ark. Mat. 49 (1) 79 - 96, April 2011. https://doi.org/10.1007/s11512-009-0117-1

Information

Received: 8 May 2009; Published: April 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1223.05201
MathSciNet: MR2784258
Digital Object Identifier: 10.1007/s11512-009-0117-1

Rights: 2010 © Institut Mittag-Leffler

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Vol.49 • No. 1 • April 2011
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