These lecture notes provide a pedagogical tour of random walk and random graph theory, covering standard results without claiming new research advances.
A Proof of the Kahn-Kalai Conjecture
1 Pith paper cite this work. Polarity classification is still indexing.
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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 $\mathcal{F}$.
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2024 1verdicts
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A random walk among random graphs
These lecture notes provide a pedagogical tour of random walk and random graph theory, covering standard results without claiming new research advances.