115 citations · 1.2k across the 68 of their papers we have counts for
4 papers · 1 filter
Near critical scaling relations for planar Bernoulli percolation without differential inequalities
Hugo Duminil-Copin, Ioan Manolescu, Vincent Tassion
We provide a new proof of the near-critical scaling relation for Bernoulli percolation on the square lattice already proved by Kesten in 1987. We rely on a novel approach…
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…
Conformal invariance of double random currents I: identification of the limit
Hugo Duminil-Copin, Marcin Lis, Wei Qian
This is the first of two papers devoted to the proof of conformal invariance of the critical double random current model on the square lattice. More precisely, we show the converge…
Conformal invariance of double random currents II: tightness and properties in the discrete
Hugo Duminil-Copin, Marcin Lis, Wei Qian
This is the second of two papers devoted to the proof of conformal invariance of the critical double random current on the square lattice. More precisely, we show convergence of lo…