Add to ORKGInternational audienceWe show that the range of a long Brownian bridge in the hyperbolic space converges after suitable renormalisation to the Brownian continuum random tree. This result is a relatively elementary consequence of • A theorem by Bougerol and Jeulin, stating that the rescaled radial process converges to the normalized Brownian excursion, • A property of invariance under re-rooting, • The hyperbolicity of the ambient space in the sense of Gromov. A similar result is obtained for the rescaled infinite Brownian loop in hyperbolic space
38 pages, 7 figuresWe study the inhomogeneous continuum random trees (ICRT) that arise as weak limit...
Consider a nearest neighbour random walk $X_n$ on the $d$-regular tree $\T_d$, where $d\geq 3$, cond...
In the first part of this dissertation, we analyze the eigenvalues of the adjacency matrices of a wi...
International audienceWe show that the range of a long Brownian bridge in the hyperbolic space conve...
The first part of this thesis concerns the area of random maps, which is a topic in between probabil...
We consider two models of random continuous trees: Lévy trees and inhomogeneous continuum random tr...
We study a configuration model on bipartite planar maps where, given $n$ even integers, one samples ...
The standard functional central limit theorem for a renewal process with finite mean and variance, r...
We show that the uniform unlabelled unrooted tree with n vertices and vertex degrees in a fixed set ...
We observe that the probability distribution of the Brownian motion with drift −cx/(1−t) where c≠1 i...
76 pages, 7 figures, improved versionWe prove that uniform random quadrangulations of the sphere wit...
Nous considérons deux modèles d’arbres aléatoires continus, à savoir les arbres de Lévy et les arbr...
International audienceWe show that, under certain natural assumptions, large random plane bipartite ...
In this article it is shown that the Brownian motion on the continuum random tree is the scaling lim...
By computations on generating functions, Szekeres proved in 1983 that the law of the diameter of a u...
38 pages, 7 figuresWe study the inhomogeneous continuum random trees (ICRT) that arise as weak limit...
Consider a nearest neighbour random walk $X_n$ on the $d$-regular tree $\T_d$, where $d\geq 3$, cond...
In the first part of this dissertation, we analyze the eigenvalues of the adjacency matrices of a wi...
International audienceWe show that the range of a long Brownian bridge in the hyperbolic space conve...
The first part of this thesis concerns the area of random maps, which is a topic in between probabil...
We consider two models of random continuous trees: Lévy trees and inhomogeneous continuum random tr...
We study a configuration model on bipartite planar maps where, given $n$ even integers, one samples ...
The standard functional central limit theorem for a renewal process with finite mean and variance, r...
We show that the uniform unlabelled unrooted tree with n vertices and vertex degrees in a fixed set ...
We observe that the probability distribution of the Brownian motion with drift −cx/(1−t) where c≠1 i...
76 pages, 7 figures, improved versionWe prove that uniform random quadrangulations of the sphere wit...
Nous considérons deux modèles d’arbres aléatoires continus, à savoir les arbres de Lévy et les arbr...
International audienceWe show that, under certain natural assumptions, large random plane bipartite ...
In this article it is shown that the Brownian motion on the continuum random tree is the scaling lim...
By computations on generating functions, Szekeres proved in 1983 that the law of the diameter of a u...
38 pages, 7 figuresWe study the inhomogeneous continuum random trees (ICRT) that arise as weak limit...
Consider a nearest neighbour random walk $X_n$ on the $d$-regular tree $\T_d$, where $d\geq 3$, cond...
In the first part of this dissertation, we analyze the eigenvalues of the adjacency matrices of a wi...