347 citations · 566 across the 22 of their papers we have counts for
27 papers
Large deviations for the CRT
Jean-François Le Gall
We establish large deviation principles both for the CRT in the Gromov-Hausdorff topology and for the CRT weighted by its mass measure in the Gromov-Hausdorff-Prohorov topology. In…
Drilling holes in the Brownian disk: The Brownian annulus
Jean-François Le Gall, Alexis Metz-Donnadieu
We give a new construction of the Brownian annulus based on removing a hull centered at the distinguished point in the free Brownian disk. We use this construction to prove that th…
Peeling the Brownian half-plane
Jean-François Le Gall, Armand Riera
We establish a new spatial Markov property of the Brownian half-plane. According to this property, if one removes a hull centered at a boundary point, the remaining space equipped…
A stochastic differential equation for local times of super-Brownian motion
Jean-François Le Gall, Edwin Perkins
We show that local times of super-Brownian motion, or of Brownian motion indexed by the Brownian tree, satisfy an explicit stochastic differential equation. Our proofs rely on both…
Spatial Markov property in Brownian disks
Jean-François Le Gall, Armand Riera
We derive a new representation of the Brownian disk in terms of a forest of labeled trees, where labels correspond to distances from a subset of the boundary. We then use this repr…
The Markov property of local times of Brownian motion indexed by the Brownian tree
Jean-François Le Gall
We consider the model of Brownian motion indexed by the Brownian tree, which has appeared in a variety of different contexts in probability, statistical physics and combinatorics.…
The volume measure of the Brownian sphere is a Hausdorff measure
Jean-François Le Gall
We prove that the volume measure of the Brownian sphere is equal to a constant multiple of the Hausdorff measure associated with the gauge function . This sh…
Separating cycles and isoperimetric inequalities in the uniform infinite planar quadrangulation
Jean-Francois Le Gall, Thomas Lehéricy
We study geometric properties of the infinite random lattice called the uniform infinite planar quadrangulation or UIPQ. We establish a precise form of a conjecture of Krikun stati…
Brownian disks and the Brownian snake
Jean-François Le Gall
We provide a new construction of the Brownian disks, which have been defined by Bettinelli and Miermont as scaling limits of quadrangulations with a boundary when the boundary size…
First-passage percolation and local modifications of distances in random triangulations
Nicolas Curien, Jean-François Le Gall
We study local modifications of the graph distance in large random triangulations. Our main results show that, in large scales, the modified distance behaves like a deterministic c…
Excursion theory for Brownian motion indexed by the Brownian tree
Céline Abraham, Jean-François Le Gall
We develop an excursion theory for Brownian motion indexed by the Brownian tree, which in many respects is analogous to the classical Itô theory for linear Brownian motion. Each ex…
Scaling limits for the peeling process on random maps
Nicolas Curien, Jean-François Le Gall
We study the scaling limit of the volume and perimeter of the discovered regions in the Markovian explorations known as peeling processes for infinite random planar maps such as th…
The hull process of the Brownian plane
Nicolas Curien, Jean-François Le Gall
We study the random metric space called the Brownian plane, which is closely related to the Brownian map and is conjectured to be the universal scaling limit of many discrete rando…
Bessel processes, the Brownian snake and super-Brownian motion
Jean-François Le Gall
We prove that, both for the Brownian snake and for super-Brownian motion in dimension one, the historical path corresponding to the minimal spatial position is a Bessel process of…
Random geometry on the sphere
Jean-François Le Gall
We introduce and study a universal model of random geometry in two dimensions. To this end, we start from a discrete graph drawn on the sphere, which is chosen uniformly at random…
The range of tree-indexed random walk in low dimensions
Jean-François Le Gall, Shen Lin
We study the range of a random walk on the -dimensional lattice indexed by a random tree with vertices. Under the assumption that the random walk is cen…
The Brownian cactus II. Upcrossings and local times of super-Brownian motion
Jean-François Le Gall
We study properties of the random metric space called the Brownian map. For every h>0, we consider the connected components of the complement of the open ball of radius h centered…
The range of tree-indexed random walk
Jean-François Le Gall, Shen Lin
We provide asymptotics for the range R(n) of a random walk on the d-dimensional lattice indexed by a random tree with n vertices. Using Kingman's subadditive ergodic theorem, we pr…
Quadrangulations with no pendant vertices
Johel Beltran, Jean-François Le Gall
We prove that the metric space associated with a uniformly distributed planar quadrangulation with n faces and no pendant vertices converges modulo a suitable rescaling to the Brow…
The harmonic measure of balls in random trees
Nicolas Curien, Jean-François Le Gall
We study properties of the harmonic measure of balls in typical large discrete trees. For a ball of radius centered at the root, we prove that, although the size of the boundar…
The Brownian plane
Nicolas Curien, Jean-François Le Gall
We introduce and study the random non-compact metric space called the Brownian plane, which is obtained as the scaling limit of the uniform infinite planar quadrangulation. Alterna…
Uniqueness and universality of the Brownian map
Jean-François Le Gall
We consider a random planar map which is uniformly distributed over the class of all rooted q-angulations with n faces. We let be the vertex set of , whic…
Scaling limits of random trees and planar maps
Jean-François Le Gall, Grégory Miermont
These are the notes for a series of lectures given at the Clay Mathematical Institute Summer School in Buzios, July 11 - August 7, 2010. We review some of the recent aspects of sca…
Random recursive triangulations of the disk via fragmentation theory
Nicolas Curien, Jean-François Le Gall
We introduce and study an infinite random triangulation of the unit disk that arises as the limit of several recursive models. This triangulation is generated by throwing chords un…