Percolation Inequalities and Decision Trees

Published 15 Aug 2024 in math.PR and math.CO | (2408.08457v2)

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

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