MATH Seminar
| Title: Upper tails for arithmetic progressions in random sets |
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| Seminar: Combinatorics |
| Speaker: Lutz Warnke of The University of Cambridge |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2015-11-13 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: We study the upper tail {\mathbb P}(X \ge (1+\varepsilon) {\mathbb E} X) of the number of arithmetic progressions of a given length in a random subset of [n]=\{1, \ldots, n\}, establishing exponential bounds for which are best possible up to constant factors in the exponent (improving results of Janson and Ruci{\'n}ski). The proof also extends to Schur triples, and, more generally, to the number of edges in random induced subhypergraphs of `almost linear' k-uniform hypergraphs. |
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