Upper tails for arithmetic progressions in random subsets
Combinatorics
2017-12-12 v1 Number Theory
Probability
Abstract
We study the upper tail of the number of arithmetic progressions of a given length in a random subset of {1,...,n}, establishing exponential bounds which are best possible up to constant factors in the exponent. 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.
Cite
@article{arxiv.1612.08559,
title = {Upper tails for arithmetic progressions in random subsets},
author = {Lutz Warnke},
journal= {arXiv preprint arXiv:1612.08559},
year = {2017}
}
Comments
28 pages. To appear in Israel Journal of Mathematics