115 citations · 1.2k across the 68 of their papers we have counts for
8 papers · 2 filters
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…
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…
Internal Diffusion-Limited aggregation with uniform starting points
Itai Benjamini, Hugo Duminil-Copin, Gady Kozma +1
We study internal diffusion-limited aggregation with random starting points on Z^d. In this model, each new particle starts from a vertex chosen uniformly at random on the existing…