Percolation Inequalities and Decision Trees

2024/08/15 by Nikita Gladkov, Gladkov, Nikita · 1 citation
Mathematics · Physics and Astronomy · #05C80 #60K35 #82B43 #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Graph theory and applications #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2408.08457

openalex publication_date 2024/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Dimension dependence of critical phenomena in long-range percolation

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