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

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

2009-05-07

arxiv.org/abs/0905.0972v1

Mathematics

Probability

15 pages

Scientific paper

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.

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