Percolation Inequalities and Decision Trees
Probability
2024-08-26 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.2408.08457,
title = {Percolation Inequalities and Decision Trees},
author = {Nikita Gladkov},
journal= {arXiv preprint arXiv:2408.08457},
year = {2024}
}
Comments
20 pages