Publications (87)
Crossing probabilities in topological rectangles for the critical planar FK-Ising model
Dmitry Chelkak, Hugo Duminil-Copin, Clément Hongler
We consider the FK-Ising model in two dimensions at criticality. We obtain bounds on crossing probabilities of arbitrary topological rectangles, uniform with respect to the boundar…
Minimal growth harmonic functions on lamplighter groups
Itai Benjamini, Hugo Duminil-Copin, Gady Kozma +1
We study the minimal possible growth of harmonic functions on lamplighters. We find that has no sublinear harmonic functions, $(\mathbb{Z}/2)\wr \mat…
Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension
Hugo Duminil-Copin, Alejandro Rivera, Pierre-François Rodriguez +1
For the Bargmann--Fock field on with , we prove that the critical level of the percolation model formed by the excursion sets is…
On the critical parameters of the random-cluster model on isoradial graphs
Vincent Beffara, Hugo Duminil-Copin, Stanislav Smirnov
The critical surface for random-cluster model with cluster-weight on isoradial graphs is identified using parafermionic observables. Correlations are also shown to decay e…
Higher order corrections for anisotropic bootstrap percolation
Hugo Duminil-Copin, Aernout C. D. van Enter, Tim Hulshof
We study the critical probability for the metastable phase transition of the two-dimensional anisotropic bootstrap percolation model with -neighbourhood and threshold $r = 3…
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…