4 papers · 1 filter
A random walk approach to high-dimensional critical phenomena
Hugo Duminil-Copin, Aman Markar, Romain Panis +1
We present a "black box" proof of mean-field near-critical behaviour for a family of functions on () satisfying a short list of assumptions. The functions repr…
An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions
Hugo Duminil-Copin, Romain Panis
This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions . Among other results, we obtain up-to-constant estimate…
An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions
Hugo Duminil-Copin, Romain Panis
This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions . We obtain an upper bound for the full-space…
New lower bounds for the (near) critical Ising and models' two-point functions
Hugo Duminil-Copin, Romain Panis
We study the nearest-neighbour Ising and models on with and obtain new lower bounds on their two-point functions at (and near) criticality. Together…