115 citations · 1.2k across the 68 of their papers we have counts for
7 papers · 1 filter
Sharp threshold phenomena in statistical physics
Hugo Duminil-Copin
This text describes the content of the Takagi lectures given by the author in Kyoto in 2017. The lectures present some aspects of the theory of sharp thresholds for boolean functio…
Bounding the number of self-avoiding walks: Hammersley-Welsh with polygon insertion
Hugo Duminil-Copin, Shirshendu Ganguly, Alan Hammond +1
Let denote the number of self-avoiding walks of length starting at the origin in the Euclidean nearest-neighbour lattice . Let $μ= \lim_n c_n^{1/n}…
Exponential decay of truncated correlations for the Ising model in any dimension for all but the critical temperature
Hugo Duminil-Copin, Subhajit Goswami, Aran Raoufi
The truncated two-point function of the ferromagnetic Ising model on () in its pure phases is proven to decay exponentially fast throughout the ordered regime…
Existence of phase transition for percolation using the Gaussian Free Field
Hugo Duminil-Copin, Subhajit Goswami, Aran Raoufi +2
In this paper, we prove that Bernoulli percolation on bounded degree graphs with isoperimetric dimension undergoes a non-trivial phase transition (in the sense that ).…
Subcritical phase of -dimensional Poisson-Boolean percolation and its vacant set
Hugo Duminil-Copin, Aran Raoufi, Vincent Tassion
We prove that the Poisson-Boolean percolation on undergoes a sharp phase transition in any dimension under the assumption that the radius distribution has a f…
On the number of maximal paths in directed last-passage percolation
Hugo Duminil-Copin, Harry Kesten, Fedor Nazarov +2
We show that the number of maximal paths in directed last-passage percolation on the hypercubic lattice in which weights take finitely many values is typ…