3 papers
math.PR2026
Rotational invariance in critical planar lattice models
Hugo Duminil-Copin, Karol Kajetan Kozlowski, Dmitry Krachun +2
We prove that the large-scale properties of a number of two-dimensional lattice models are rotationally invariant. More precisely, we prove that the random-cluster model on the squ…
math.PR2026
Critical exponents for planar random-cluster model with cluster-weight
Hong-Bin Chen, Hugo Duminil-Copin, Tiancheng He +4
Using the Baxter-Kelland-Wu coupling and the convergence of the height function of the six-vertex model to the Gaussian Free Field, we extract critical exponents for the planar cri…
math.PR2025
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…