1 citations · 2 across the 4 of their papers we have counts for
4 papers
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…
Exploring mazes at random
Nikita Gladkov, Igor Pak
We consider a probabilistic version of the depth-first search on mazes with two exits, and show that this algorithm has equal probability of finding either exit. The proof is combi…
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…
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…