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
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
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