47 citations · 124 across the 20 of their papers we have counts for
21 papers
Two-dimensional forest fires with boundary ignitions
Jacob van den Berg, Pierre Nolin
In the classical Drossel-Schwabl forest fire process, vertices of a lattice become occupied at rate , and they are hit by lightning at some tiny rate , which causes entire…
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…
Near-critical avalanches in 2D frozen percolation and forest fires
Wai-Kit Lam, Pierre Nolin
We study two closely related processes on the triangular lattice: frozen percolation, where connected components of occupied vertices freeze (they stop growing) as soon as they con…
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…
No exceptional words for Bernoulli percolation
Pierre Nolin, Vincent Tassion, Augusto Teixeira
Benjamini and Kesten introduced in 1995 the problem of embedding infinite binary sequences into a Bernoulli percolation configuration, known as "percolation of words". We give a po…
Near-critical percolation with heavy-tailed impurities, forest fires and frozen percolation
Jacob van den Berg, Pierre Nolin
Consider critical site percolation on a "nice" planar lattice: each vertex is occupied with probability , and vacant with probability . Now, suppose that addition…