Arkiv för Matematik

Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs

Svante Janson and Andrzej Ruciński

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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.

Note

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.

Article information

Source
Ark. Mat., Volume 49, Number 1 (2011), 79-96.

Dates
Received: 8 May 2009
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907128

Digital Object Identifier
doi:10.1007/s11512-009-0117-1

Mathematical Reviews number (MathSciNet)
MR2784258

Zentralblatt MATH identifier
1223.05201

Rights
2010 © Institut Mittag-Leffler

Citation

Janson, Svante; Ruciński, Andrzej. Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs. Ark. Mat. 49 (2011), no. 1, 79--96. doi:10.1007/s11512-009-0117-1. https://projecteuclid.org/euclid.afm/1485907128


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References

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