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arxiv: 2408.08457 · v2 · pith:XJ5QXSJ5 · submitted 2024-08-15 · math.PR · math.CO

Percolation Inequalities and Decision Trees

Nikita Gladkov This is my paper

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classification math.PR math.CO
keywords inequalitiesdecisionpercolationtreesappliedberg--kestenbernoullibond
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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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