English

A simple proof of the non-uniform Kahn-Kalai conjecture

Combinatorics 2023-06-23 v1

Abstract

We revisit the Kahn-Kalai conjecture, recently proved in striking fashion by Park and Pham, and present a slightly reformulated simple proof which has a few advantages: (1) it works for non-uniform product measures, (2) it gives near-optimal bounds even for sampling probabilities close to 1, (3) it gives a clean bound of pc4qclog2(7)p_c \leq 4q_c \log_2 (7\ell) for every \ell-bounded set system, 1\ell\geq 1.

Keywords

Cite

@article{arxiv.2306.12576,
  title  = {A simple proof of the non-uniform Kahn-Kalai conjecture},
  author = {Bryan Park and Jan Vondrák},
  journal= {arXiv preprint arXiv:2306.12576},
  year   = {2023}
}