43 citations · 108 across the 12 of their papers we have counts for
12 papers
Geometric properties of spin clusters in random triangulations coupled with an Ising Model
Marie Albenque, Laurent Ménard
We investigate the geometry of a typical spin cluster in random triangulations sampled with a probability proportional to the energy of an Ising configuration on their vertices, bo…
Percolation probability and critical exponents for site percolation on the UIPT
Laurent Ménard
We derive three critical exponents for Bernoulli site percolation on the on the Uniform Infinite Planar Triangulation (UIPT). First we compute explicitly the probability that the r…
Long induced paths in a configuration model
Nathanaël Enriquez, Gabriel Faraud, Laurent Ménard +1
In an article published in 1987 in Combinatorica \cite{MR918397}, Frieze and Jackson established a lower bound on the length of the longest induced path (and cycle) in a sparse ran…
Depth First Exploration of a Configuration Model
Nathanaël Enriquez, Gabriel Faraud, Laurent Ménard +1
We introduce an algorithm that constructs a random uniform graph with prescribed degree sequence together with a depth first exploration of it. In the so-called supercritical regim…
Local convergence of large random triangulations coupled with an Ising model
Marie Albenque, Laurent Ménard, Gilles Schaeffer
We prove the existence of the local weak limit of the measure obtained by sampling random triangulations of size decorated by an Ising configuration with a weight proportional…
The skeleton of the UIPT, seen from infinity
Nicolas Curien, Laurent Ménard
We prove that geodesic rays in the Uniform Infinite Planar Triangulation (UIPT) coalesce in a strong sense using the skeleton decomposition of random triangulations discovered by K…
Limiting shape of the Depth First Search tree in an Erdős-Rényi graph
Nathanaël Enriquez, Gabriel Faraud, Laurent Ménard
We show that the profile of the tree constructed by the Depth First Search Algorithm in the giant component of an Erdős-Rényi graph with vertices and connection probability $c/…
Asymptotic expansion of the expected spectral measure of Wigner matrices
Nathanaël Enriquez, Laurent Ménard
We compute an asymptotic expansion with precision 1/n of the moments of the expected empirical spectral measure of Wigner matrices of size n with independent centered entries. We i…
Percolation by cumulative merging and phase transition for the contact process on random graphs
Laurent Ménard, Arvind Singh
Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both cl…
Percolation on uniform infinite planar maps
Laurent Ménard, Pierre Nolin
We construct the uniform infinite planar map (UIPM), obtained as the n \to \infty local limit of planar maps with n edges, chosen uniformly at random. We then describe how the UIPM…
A view from infinity of the uniform infinite planar quadrangulation
Nicolas Curien, Laurent Ménard, Grégory Miermont
We introduce a new construction of the Uniform Infinite Planar Quadrangulation (UIPQ). Our approach is based on an extension of the Cori-Vauquelin-Schaeffer mapping in the context…
Scaling limits for the uniform infinite quadrangulation
Jean-François Le Gall, Laurent Ménard
The uniform infinite planar quadrangulation is an infinite random graph embedded in the plane, which is the local limit of uniformly distributed finite quadrangulations with a fixe…