20 citations · 83 across the 15 of their papers we have counts for
13 papers · 1 filter
Double cluster swapping for spin models: Pfaffian relations and sharpness
Diederik van Engelenburg, Lorca Heeney, Marcin Lis
We introduce and study a new geometric representation for general classical spin models. It consists of two coupled percolation configurations that are the joint FK (random cluster…
The Ising magnetisation field and the Gaussian free field
Tomás Alcalde López, Lorca Heeney, Marcin Lis
We construct a natural coupling between the continuum Gaussian free field (GFF) and the critical Ising magnetisation field (IMF) in a planar domain. In fact, we show that two indep…
Uniform spanning trees and random matrix statistics
Nathanaël Berestycki, Marcin Lis, Mingchang Liu +1
We consider a uniform spanning tree in a -square grid approximation of a planar domain . For given integer , we condition the tree on the following -arm event: we…
Conformally invariant boundary arcs in double dimers
Marcin Lis, Lucas Rey, Kieran Ryan
We consider two different versions of the double dimer model on a planar domain, where we either fold a single dimer cover on a symmetric domain onto itself across the line of symm…
On the duality between height functions and continuous spin models
Diederik van Engelenburg, Marcin Lis
We revisit the classical phenomenon of duality between random integer-valued height functions with positive definite potentials and abelian spin models with O(2) symmetry. We use i…
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…
Conformal invariance of double random currents II: tightness and properties in the discrete
Hugo Duminil-Copin, Marcin Lis, Wei Qian
This is the second of two papers devoted to the proof of conformal invariance of the critical double random current on the square lattice. More precisely, we show convergence of lo…
Free boundary dimers: random walk representation and scaling limit
Nathanael Berestycki, Marcin Lis, Wei Qian
We study the dimer model on subgraphs of the square lattice in which vertices on a prescribed part of the boundary (the free boundary) are possibly unmatched. Each such unmatched v…
On delocalization in the six-vertex model
Marcin Lis
We show that the six-vertex model with parameter on a square lattice torus has an ergodic infinite-volume limit as the size of the torus grows to infinity. Moreo…
Spins, percolation and height functions
Marcin Lis
To highlight certain similarities in combinatorial representations of several well known two-dimensional models of statistical mechanics, we introduce and study a new family of mod…
The planar Ising model and total positivity
Marcin Lis
A matrix is called totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative). Consider the Ising model with free boundary conditions and no ex…
Gaussian approximation of moments of sums of independent random variables
Marcin Lis
We continue the research of Latała on improving estimates of -th moments of sums of independent random variables. We generalize some of his results in the case when $2 \leq p \l…
Random walk loop soups and conformal loop ensembles
Tim van de Brug, Federico Camia, Marcin Lis
The random walk loop soup is a Poissonian ensemble of lattice loops; it has been extensively studied because of its connections to the discrete Gaussian free field, but was origina…