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arXiv · 2408.08457

Percolation Inequalities and Decision Trees

Nikita Gladkov
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Abstract

The use of decision trees for percolation inequalities started with the celebrated O'Donnell--Saks--Schramm--Servedio (OSSS) inequality. We prove decision tree generalizations of the Harris--Kleitman (HK), van den Berg--Kesten (vdBK), and other inequalities. These inequalities are then applied to estimate the connection probabilities in Bernoulli bond percolation on general graphs.

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Nikita Gladkov. 2024-08-15. Percolation Inequalities and Decision Trees. https://arxiv.org/abs/2408.08457

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