5 citations · 5 across the 3 of their papers we have counts for
6 papers
Maximum displacement of critical centered branching random walks under minimal assumptions
Thomas Lehéricy
We study the critical centered branching random walk with offspring and displacement distributions having finite variance, under minimal assumptions on its structure. We show that…
Random cubic planar graphs converge to the Brownian sphere
Marie Albenque, Éric Fusy, Thomas Lehéricy
In this paper, the scaling limit of random connected cubic planar graphs (respectively multigraphs) is shown to be the Brownian sphere. The proof consists in essentially two main s…
Uniform mixing time and bottlenecks in uniform finite quadrangulations
Thomas Lehéricy
We prove a lower bound on the size of bottlenecks in uniform quadrangulations, valid at all scales simultaneously. We use it to establish upper bounds on the uniform mixing time of…
Recurrence of the Uniform Infinite Half-Plane Map via duality of resistances
Thomas Budzinski, Thomas Lehéricy
We study the simple random walk on the Uniform Infinite Half-Plane Map, which is the local limit of critical Boltzmann planar maps with a large and simple boundary. We prove that t…
First-passage percolation in random planar maps and Tutte's bijection
Thomas Lehéricy
We consider large random planar maps and study the first-passage percolation distance obtained by assigning independent identically distributed lengths to the edges. We consider th…
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…