Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs |
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| Authors: | Svante Janson Andrzej Ruciński |
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| Institution: | 1.Department of Mathematics,Uppsala University,Uppsala,Sweden;2.Department of Discrete Mathematics,Adam Mickiewicz University,Poznań,Poland |
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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. |
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