115 citations · 1.2k across the 68 of their papers we have counts for
6 papers · 1 filter
Convergence of Ising interfaces to Schramm's SLE curves
Dmitry Chelkak, Hugo Duminil-Copin, Clément Hongler +2
We show how to combine our earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schramm's SLE…
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…
Random Currents and Continuity of Ising Model's Spontaneous Magnetization
Michael Aizenman, Hugo Duminil-Copin, Vladas Sidoravicius
The spontaneous magnetization is proved to vanish continuously at the critical temperature for a class of ferromagnetic Ising spin systems which includes the nearest neighbor ferro…
Limit of the Wulff Crystal when approaching criticality for site percolation on the triangular lattice
Hugo Duminil-Copin
The understanding of site percolation on the triangular lattice progressed greatly in the last decade. Smirnov proved conformal invariance of critical percolation, thus paving the…
On the probability that self-avoiding walk ends at a given point
Hugo Duminil-Copin, Alexander Glazman, Alan Hammond +1
We prove two results on the delocalization of the endpoint of a uniform self-avoiding walk on Z^d for d>1. We show that the probability that a walk of length n ends at a point x te…
Seven-dimensional forest fires
Daniel Ahlberg, Hugo Duminil-Copin, Gady Kozma +1
We show that in high dimensional Bernoulli percolation, removing from a thin infinite cluster a much thinner infinite cluster leaves an infinite component. This observation has imp…