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

2010; Mittag-Leffler Institute; Volume: 49; Issue: 1 Linguagem: Inglês

10.1007/s11512-009-0117-1

1871-2487

Svante Janson, Andrzej Ruciński,

Markov Chains and Monte Carlo Methods

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.