115 citations · 1.2k across the 68 of their papers we have counts for
5 papers · 2 filters
Disorder, entropy and harmonic functions
Itai Benjamini, Hugo Duminil-Copin, Gady Kozma +1
We study harmonic functions on random environments with particular emphasis on the case of the infinite cluster of supercritical percolation on . We prove that the ve…
The near-critical planar FK-Ising model
Hugo Duminil-Copin, Christophe Garban, Gábor Pete
We study the near-critical FK-Ising model. First, a determination of the correlation length defined via crossing probabilities is provided. Second, a phenomenon about the near-crit…
Supercritical self-avoiding walks are space-filling
Hugo Duminil-Copin, Gady Kozma, Ariel Yadin
We consider random self-avoiding walks between two points on the boundary of a finite subdomain of Z^d (the probability of a self-avoiding trajectory gamma is proportional to mu^{-…
Conformal invariance of lattice models
Hugo Duminil-Copin, Stanislav Smirnov
These lecture notes provide a (almost) self-contained account on conformal invariance of the planar critical Ising and FK-Ising models. They present the theory of discrete holomorp…
Planar percolation with a glimpse of Schramm-Loewner Evolution
Vincent Beffara, Hugo Duminil-Copin
In recent years, important progress has been made in the field of two-dimensional statistical physics. One of the most striking achievements is the proof of the Cardy-Smirnov formu…