Geodesic
The Park-Pham theorem with optimal convergence rate
Tolson Bell1
1Carnegie Mellon University
The electronic journal of combinatorics, Tome 30 (2023) no. 2
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Park and Pham's recent proof of the Kahn-Kalai conjecture was a major breakthrough in the field of graph and hypergraph thresholds. Their result gives an upper bound on the threshold at which a probabilistic construction has a $1-\epsilon$ chance of achieving a given monotone property. While their bound in other parameters is optimal up to constant factors for any fixed $\epsilon$, it does not have the optimal dependence on $\epsilon$ as $\epsilon\rightarrow 0$. In this short paper, we prove a version of the Park-Pham Theorem with optimal $\epsilon$-dependence.
DOI : 10.37236/11600
Classification : 05D05, 05D40
Mots-clés : Kahn-Kalai conjecture

Tolson Bell  1

1 Carnegie Mellon University 
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Tolson Bell. The Park-Pham theorem with optimal convergence rate. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11600

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