Hugo Duminil-Copin

collaborators

5 papers

math.PR2026

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 $Z^{d}$ ( $d > 2$ ) satisfying a short list of assumptions. The functions repr…

math-ph2026

Gaussian free field convergence of the six-vertex model with $- 1 \leq I^ \leq - \frac{1}{2}$

Hugo Duminil-Copin, Karol Kajetan Kozlowski, Piet Lammers +1

We study the isotropic six-vertex model on $Z^{2}$ with spectral parameter $I^ \in [- 1, - 1/2]$ , that is, with weights $a = b = 1$ and $c \in [3, 2]$ .…

math.PR2025

An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions $d > 4$

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 $d > 4$ . Among other results, we obtain up-to-constant estimate…

math.PR2025

An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d > 6$

Hugo Duminil-Copin, Romain Panis

This article proposes a new way of deriving mean-field exponents for sufficiently spread-out Bernoulli percolation in dimensions $d > 6$ . We obtain an upper bound for the full-space…

math.PR2025

New lower bounds for the (near) critical Ising and $I ¨ ^{4}$ models' two-point functions

Hugo Duminil-Copin, Romain Panis

We study the nearest-neighbour Ising and $I ¨ ^{4}$ models on $Z^{d}$ with $d \geq 3$ and obtain new lower bounds on their two-point functions at (and near) criticality. Together…

A random walk approach to high-dimensional critical phenomena

Gaussian free field convergence of the six-vertex model with −1≤I^≤−21​

An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions d>4

An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions d>6

New lower bounds for the (near) critical Ising and I¨4 models' two-point functions

Gaussian free field convergence of the six-vertex model with $- 1 \leq I^ \leq - \frac{1}{2}$

An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions $d > 4$

An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d > 6$

New lower bounds for the (near) critical Ising and $I ¨ ^{4}$ models' two-point functions