4 papers · 1 filter
Percolation of discrete GFF in dimension two I. Arm events in the random walk loop soup
Yifan Gao, Pierre Nolin, Wei Qian
In this work, which is the first part of a series of two papers, we study the random walk loop soup in dimension two. More specifically, we estimate the probability that two large…
Boundary rules and breaking of self-organized criticality in 2D frozen percolation
Jacob van den Berg, Pierre Nolin
We study frozen percolation on the (planar) triangular lattice, where connected components stop growing ("freeze") as soon as their "size" becomes at least , for some parameter…
Two-dimensional volume-frozen percolation: exceptional scales
Jacob van den Berg, Pierre Nolin
We study a percolation model on the square lattice, where clusters "freeze" (stop growing) as soon as their volume (i.e. the number of sites they contain) gets larger than N, the p…
A percolation process on the square lattice where large finite clusters are frozen
Jacob van den Berg, Bernardo N. B. de Lima, Pierre Nolin
Aldous constructed a growth process for the binary tree where clusters freeze as soon as they become infinite. It was pointed out by Benjamini and Schramm that such a process does…