32 citations · 49 across the 13 of their papers we have counts for
14 papers · 1 filter
Dense and nondense limits for uniform random intersection graphs
Frédérique Bassino, Mathilde Bouvel, Valentin Féray +2
We obtain the scaling limits of random graphs drawn uniformly in three families of intersection graphs: permutation graphs, circle graphs, and unit interval graphs. The two first f…
Scaling limit of graph classes through split decomposition
Frédérique Bassino, Mathilde Bouvel, Valentin Féray +2
We prove that Aldous' Brownian CRT is the scaling limit, with respect to the Gromov--Prokhorov topology, of uniform random graphs in each of the three following families of graphs:…
Longest increasing paths with Lipschitz constraints
Anne-Laure Basdevant, Lucas Gerin
The Hammersley problem asks for the maximal number of points in a monotonous path through a Poisson point process. It is exactly solvable and notoriously known to belong to the KPZ…
Scaling limits of permutation classes with a finite specification: a dichotomy
Frédérique Bassino, Mathilde Bouvel, Valentin Féray +3
We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) al…
Longest increasing paths with gaps
Anne-Laure Basdevant, Lucas Gerin
We consider a variant of the continuous and discrete Ulam-Hammersley problems: we study the maximal length of an increasing path through a Poisson point process (or a Bernoulli poi…
Universal limits of substitution-closed permutation classes
Frédérique Bassino, Mathilde Bouvel, Valentin Féray +3
We consider uniform random permutations in proper substitution-closed classes and study their limiting behavior in the sense of permutons. The limit depends on the generating serie…
The Brownian limit of separable permutations
Frédérique Bassino, Mathilde Bouvel, Valentin Féray +2
We study random uniform permutations in an important class of pattern-avoiding permutations: the separable permutations. We describe the asymptotics of the number of occurrences of…
Discrete Hammersley's Lines with sources and sinks
A. -L. Basdevant, N. Enriquez, L. Gerin +1
We introduce two stationary versions of two discrete variants of Hammersley's process in a finite box, this allows us to recover in a unified and simple way the laws of large numbe…
The Page-R{é}nyi parking process
Lucas Gerin
In the Page parking (or packing) model on a discrete interval (also known as the discrete R{é}nyi packing problem or the unfriendly seating problem), cars of length two successivel…
The shape of large balls in highly supercritical percolation
Anne-Laure Basdevant, Nathanaël Enriquez, Lucas Gerin +1
We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on . This shows that when…
Distances in the highly supercritical percolation cluster
Anne-Laure Basdevant, Nathanaël Enriquez, Lucas Gerin
On the supercritical percolation cluster with parameter p, the distances between two distant points of the axis are asymptotically increased by a factor 1+(1-p)/2+o(1-p) with respe…
A Branching-selection process related to censored Galton-Walton processes
Olivier Couronné, Lucas Gerin
We obtain the asymptotics for the speed of a particular case of a particle system with branching and selection introduced by Bérard and Gouéré (2010). The proof is based on a conne…
Construction of a short path in high dimensional First Passage Percolation
Olivier Couronné, Nathanaël Enriquez, Lucas Gerin
For First Passage Percolation in Z^d with large d, we construct a path connecting the origin to {x_1 =1}, whose passage time has optimal order \log d/d. Besides, an improved lower…
Random sampling of lattice paths with constraints, via transportation
Lucas Gerin
We discuss a Monte Carlo Markov Chain (MCMC) procedure for the random sampling of some one-dimensional lattice paths with constraints, for various constraints. We show that an appr…