3 papers
math.PR2024
Percolation Inequalities and Decision Trees
Nikita Gladkov
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 t…
math.PR2023
Positive dependence for colored percolation
Nikita Gladkov, Igor Pak
For uniform random 4-colorings of graph edges with colors a,b,c,d, every two colors form a 1/2-percolation, and every two overlapping pairs of colors form independent 1/2-percolati…
math.PR2023
A strong FKG inequality for multiple events
Nikita Gladkov
We give an extension of the FKG inequality to the case of multiple events with equal pairwise intersections. We then apply this inequality to resolve Kahn's question on positive as…