115 citations · 1.2k across the 68 of their papers we have counts for
4 papers · 2 filters
Conformal invariance of crossing probabilities for the Ising model with free boundary conditions
Stéphane Benoist, Hugo Duminil-Copin, Clément Hongler
We prove that crossing probabilities for the critical planar Ising model with free boundary conditions are conformally invariant in the scaling limit, a phenomenon first investigat…
The phase transitions of the planar random-cluster and Potts models with q larger than 1 are sharp
Hugo Duminil-Copin, Ioan Manolescu
We prove that random-cluster models with q larger than 1 on a variety of planar lattices have a sharp phase transition, that is that there exists some parameter p_c below which the…
A quantitative Burton-Keane estimate under strong FKG condition
Hugo Duminil-Copin, Dmitry Ioffe, Yvan Velenik
We consider translationally-invariant percolation models on satisfying the finite energy and the FKG properties. We provide explicit upper bounds on the probability…
Universality for two-dimensional critical cellular automata
Béla Bollobás, Hugo Duminil-Copin, Robert Morris +1
We study the class of monotone, two-state, deterministic cellular automata, in which sites are activated (or 'infected') by certain configurations of nearby infected sites. These m…