2 papers
math.PR2026
Bond percolation does not simulate site percolation
Nikita Gladkov, Aleksandr Zimin
We show that a site percolation is a stronger model than a bond percolation. We use the van den Berg -- Kesten (vdBK) inequality to prove that site percolation on a neighborhood of…
math.CO2024
The bunkbed conjecture is false
Nikita Gladkov, Igor Pak, Aleksandr Zimin
We give an explicit counterexample to the Bunkbed Conjecture introduced by Kasteleyn in 1985. The counterexample is given by a planar graph on vertices, and is built on the…