8 citations · 13 across the 12 of their papers we have counts for
12 papers
A 2D forest fire process beyond the critical time
Jacob van den Berg, Pierre Nolin
We study forest fire processes in two dimensions. On a given planar lattice, vertices independently switch from vacant to occupied at rate (initially they are all vacant), and…
An upper bound on the two-arms exponent for critical percolation on
Jacob van den Berg, Diederik van Engelenburg
Consider critical site percolation on with . Cerf (2015) pointed out that from classical work by Aizenman, Kesten and Newman (1987) and Gandolfi, Grimmett…
On the four-arm exponent for 2D percolation at criticality
Jacob van den Berg, Pierre Nolin
For two-dimensional percolation at criticality, we discuss the inequality for the polychromatic four-arm exponent (and stronger versions, the strongest so far being $α_4…
A lower bound for point-to-point connection probabilities in critical percolation
J. van den Berg, H. Don
Consider critical site percolation on with . We prove a lower bound of order for point-to-point connection probabilities, where is the dist…
On the size of the largest cluster in 2D critical percolation
Jacob van den Berg, Rene Conijn
We consider (near-)critical percolation on the square lattice. Let M_n be the size of the largest open cluster contained in the box [-n,n]^2, and let pi(n) be the probability that…
A percolation process on the binary tree where large finite clusters are frozen
Jacob van den Berg, Demeter Kiss, Pierre Nolin
We study a percolation process on the planted binary tree, where clusters freeze as soon as they become larger than some fixed parameter N. We show that as N goes to infinity, the…