English

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.

Keywords

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

R2 v1 2026-06-22T17:34:58.680Z