115 citations · 1.2k across the 68 of their papers we have counts for
9 papers · 1 filter
Sixty years of percolation
Hugo Duminil-Copin
Percolation models describe the inside of a porous material. The theory emerged timidly in the middle of the twentieth century before becoming one of the major objects of interest…
On the double random current nesting field
Hugo Duminil-Copin, Marcin Lis
We relate the planar random current representation introduced by Griffiths, Hurst and Sherman to the dimer model. More precisely, we provide a measure-preserving map between double…
Universality for the random-cluster model on isoradial graphs
Hugo Duminil-Copin, Jhih-Huang Li, Ioan Manolescu
We show that the canonical random-cluster measure associated to isoradial graphs is critical for all . Additionally, we prove that the phase transition of the model is of…
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…
Lectures on the Ising and Potts models on the hypercubic lattice
Hugo Duminil-Copin
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite…
Macroscopic loops in the loop model at Nienhuis' critical point
Hugo Duminil-Copin, Alexander Glazman, Ron Peled +1
The loop model is a model for a random collection of non-intersecting loops on the hexagonal lattice, which is believed to be in the same universality class as the spin $O(n…