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arXiv · 2306.12576

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

Bryan Park·Jan Vondrák
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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 $p_c \leq 4q_c \log_2 (7\ell)$ for every $\ell$-bounded set system, $\ell\geq 1$.

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Bryan Park, Jan Vondrák. 2023-06-21. A simple proof of the non-uniform Kahn-Kalai conjecture. https://arxiv.org/abs/2306.12576

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