arXiv:2203.17207math.CO
A Proof of the Kahn-Kalai Conjecture
Abstract
Proving the ``expectation-threshold'' conjecture of Kahn and Kalai, we show that for any increasing property $\mathcal{F}$ on a finite set $X$, $$p_c(\mathcal{F})=O(q(\mathcal{F})\log \ell(\mathcal{F})),$$ where $p_c(\mathcal{F})$ and $q(\mathcal{F})$ are the threshold and ``expectation threshold'' of $\mathcal{F}$, and $\ell(\mathcal{F})$ is the maximum of $2$ and the maximum size of a minimal member of $\mathcal{F}$.
> I define science as anything that is scientifically rigorous That's not a definition, it's a circular statement with no information. Please provide a real and functional definition that can be used to identify whether a subject is scientifically rigorous or not. Your first…
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> That's not a definition, it's a circular statement with no information. Common man do you want me to copy-paste the definition of science from wikipedia here? You can look it up yourself. My obvious statement is that the problem I see is that some stuff that people want to…
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