5 papers · 1 filter
Uniform analyticity of local observables in FK-percolation and analyticity of the Ising spontaneous magnetisation
Lucas D'Alimonte, Loïc Gassmann
We prove that, in the FK-percolation model, the probabilities of local events are uniformly analytic in the percolation parameter under suitable mixing assumptions on the measu…
Free energy analyticity of the disordered XY model and Debye screening in the 2D Coulomb gas
Lucas D'Alimonte, Piet Lammers
We consider three models of statistical mechanics: the classical XY model in arbitrary dimension, the lattice Coulomb gas in dimension two, and the square well model in arbitrary d…
Near-critical Ornstein--Zernike theory for the planar random-cluster model
Lucas D'Alimonte, Ioan Manolescu
We develop an Ornstein--Zernike theory for the two-dimensional random-cluster model with that also applies in its near-critical regime. In particular, we prove an asy…
Exact cube-root fluctuations in an area-constrained random walk model
Lucas D'Alimonte, Romain Panis
This article is devoted to the study of the behaviour of a (1+1)-dimensional model of random walk conditioned to enclose an area of order . Such a conditioning enforces a glob…
Entropic repulsion and scaling limit for a finite number of non-intersecting subcritical FK interfaces
Lucas D'Alimonte
This article is devoted to the study of a finite system of long clusters of subcritical 2-dimensional FK-percolation with q 1, conditioned on mutual avoidance. We show that…