112 citations · 389 across the 32 of their papers we have counts for
36 papers · 1 filter
Supercritical sharpness of percolation
Sahar Diskin, Philip Easo, Ritvik Ramanan Radhakrishnan +2
We prove that for supercritical percolation on every infinite transitive graph, the probability that the origin belongs to a finite cluster of size at least decays exponentiall…
Noise sensitivity of crossings for high temperature Ising model
Vincent Tassion, Hugo Vanneuville
Consider the event that there is a crossing from left to right in a box for the Ising model on the triangular lattice. We show that this event is noise sensitive under Glauber…
Counting minimal cutsets and
Philip Easo, Franco Severo, Vincent Tassion
We prove two results concerning percolation on general graphs. - We establish the converse of the classical Peierls argument: if the critical parameter for (uniform) percolation sa…
Strict inequalities for arm exponents in planar percolation
Ritvik Ramanan Radhakrishnan, Vincent Tassion
We discuss a general method to prove quantitative improvements on correlation inequalities and apply it to arm estimates for Bernoulli bond percolation on the square lattice. Our f…
Almost sharp sharpness for Poisson Boolean percolation
Barbara Dembin, Vincent Tassion
We consider Poisson Boolean percolation on with power-law distribution on the radius with a finite -moment for . We prove that subcritical sharpness occurs…
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…
Near critical scaling relations for planar Bernoulli percolation without differential inequalities
Hugo Duminil-Copin, Ioan Manolescu, Vincent Tassion
We provide a new proof of the near-critical scaling relation for Bernoulli percolation on the square lattice already proved by Kesten in 1987. We rely on a novel approach…
Supercritical percolation on graphs of polynomial growth
Daniel Contreras, Sébastien Martineau, Vincent Tassion
We consider Bernoulli percolation on transitive graphs of polynomial growth. In the subcritical regime (), it is well known that the connection probabilities decay exponenti…
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…
Long-range models in 1D revisited
Hugo Duminil-Copin, Christophe Garban, Vincent Tassion
In this short note, we revisit a number of classical result{s} on long-range 1D percolation, Ising model and Potts models [FS82, NS86, ACCN88, IN88]. More precisely, we show that f…
Noise sensitivity of percolation via differential inequalities
Vincent Tassion, Hugo Vanneuville
Consider critical Bernoulli percolation in the plane. We give a new proof of the sharp noise sensitivity theorem shown by Garban, Pete and Schramm. Contrary to the previous approac…
Planar random-cluster model: fractal properties of the critical phase
Hugo Duminil-Copin, Ioan Manolescu, Vincent Tassion
This paper is studying the critical regime of the planar random-cluster model on with cluster-weight . More precisely, we prove crossing estimates in quads…
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…
A note on Schramm's locality conjecture for random-cluster models
Hugo Duminil-Copin, Vincent Tassion
In this note, we discuss a generalization of Schramm's locality conjecture to the case of random-cluster models. We give some partial (modest) answers, and present several related…
Existence of an unbounded vacant set for subcritical continuum percolation
Daniel Ahlberg, Vincent Tassion, Augusto Teixeira
We consider the Poisson Boolean percolation model in , where the radii of each ball is independently chosen according to some probability measure with finite second m…
Exponential decay of connection probabilities for subcritical Voronoi percolation in
Hugo Duminil-Copin, Aran Raoufi, Vincent Tassion
We prove that for Voronoi percolation on , there exists such that - for , there exists such that $\mathbb{P}_p[0\text{ connected to dista…
Sharp phase transition for the random-cluster and Potts models via decision trees
Hugo Duminil-Copin, Aran Raoufi, Vincent Tassion
We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number…
The Bethe ansatz for the six-vertex and XXZ models: an exposition
Hugo Duminil-Copin, Maxime Gagnebin, Matan Harel +2
In this paper, we review a few known facts on the coordinate Bethe ansatz. We present a detailed construction of the Bethe ansatz vector and energy , which satisfy …
Discontinuity of the phase transition for the planar random-cluster and Potts models with
Hugo Duminil-Copin, Maxime Gagnebin, Matan Harel +2
We prove that the -state Potts model and the random-cluster model with cluster weight undergo a discontinuous phase transition on the square lattice. More precisely, we sh…
The box-crossing property for critical two-dimensional oriented percolation
Hugo Duminil-Copin, Vincent Tassion, Augusto Teixeira
We consider critical oriented Bernoulli percolation on the square lattice . We prove a Russo-Seymour-Welsh type result which allows us to derive several new results c…
Sharpness of the phase transition for continuum percolation in R^2
Daniel Ahlberg, Vincent Tassion, Augusto Teixeira
We study the phase transition of random radii Poisson Boolean percolation: Around each point of a planar Poisson point process, we draw a disc of random radius, independently for e…