6 citations · 11 across the 9 of their papers we have counts for
13 papers · 1 filter
Locality of percolation for graphs with polynomial growth
Daniel Contreras, Sébastien Martineau, Vincent Tassion
Schramm's Locality Conjecture asserts that the value of the critical percolation parameter of a graph satisfying depends only on its local structure. In this note, we…
Crossing probabilities for planar percolation
Laurin Köhler-Schindler, Vincent Tassion
We prove a general Russo-Seymour-Welsh result valid for any invariant planar percolation process satisfying positive association. This means that the probability of crossing a rect…
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…
Upper bounds on the percolation correlation length
Hugo Duminil-Copin, Gady Kozma, Vincent Tassion
We study the size of the near-critical window for Bernoulli percolation on . More precisely, we use a quantitative Grimmett-Marstrand theorem to prove that the correla…
Renormalization of crossing probabilities in the planar random-cluster model
Hugo Duminil-Copin, Vincent Tassion
The study of crossing probabilities - i.e. probabilities of existence of paths crossing rectangles - has been at the heart of the theory of two-dimensional percolation since its be…
Subcritical phase of -dimensional Poisson-Boolean percolation and its vacant set
Hugo Duminil-Copin, Aran Raoufi, Vincent Tassion
We prove that the Poisson-Boolean percolation on undergoes a sharp phase transition in any dimension under the assumption that the radius distribution has a f…