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

Svante Janson Department of Mathematics, Uppsala University Andrzej Ruciński Department of Discrete Mathematics, Adam Mickiewicz University

Optimization and Control Probability mathscidoc:1701.27001

Arkiv for Matematik, 49, (1), 79-96, 2009.5
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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@inproceedings{svante2009upper,
  title={Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs},
  author={Svante Janson, and Andrzej Ruciński},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203629097569992},
  booktitle={Arkiv for Matematik},
  volume={49},
  number={1},
  pages={79-96},
  year={2009},
}
Svante Janson, and Andrzej Ruciński. Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs. 2009. Vol. 49. In Arkiv for Matematik. pp.79-96. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203629097569992.
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