Exposants critiques pour le mouvement brownien et les marches aléatoires
Applications du temps local aux équations différentielles stochastiques unidimensionnelles
Sur la mesure de Hausdorff de la courbe brownienne
Sur les fonctions polaires pour le mouvement brownien
Sur le temps local d'intersection du mouvement brownien plan et la méthode de renormalisation de Varadhan
Marches aléatoires, mouvement brownien et processus de branchement
Temps locaux d'intersection et points multiples des processus de Lévy
Une approche élémentaire des théorèmes de décomposition de Williams
Marches aléatoires auto-évitantes et mesures de polymères
Exponential moments for the renormalized self-intersection local time of planar brownian motion
Paul Lévy et le mouvement brownien
Ce texte est tiré d’un exposé présenté au cours de la journée Paul Lévy organisée au Laboratoire de Probabilités et Modèles Aléatoires de l’Université Pierre et Marie Curie le 15 décembre 2011. L’objectif de cet exposé était de donner un aperçu des contributions de Paul Lévy à la théorie du mouvement brownien.
Puissances du champ d'occupation du mouvement brownien plan et applications
Hitting probabilities and potential theory for the brownian path-valued process
We consider the Brownian path-valued process studied in [LG1], [LG2], which is closely related to super Brownian motion. We obtain several potential-theoretic results related to this process. In particular, we give an explicit description of the capacitary distribution of certain subsets of the path space, such as the set of paths that hit a given closed set. These capacitary distributions are characterized as the laws of solutions of certain stochastic differential equations. They solve variational...
Random real trees
We survey recent developments about random real trees, whose prototype is the Continuum Random Tree (CRT) introduced by Aldous in 1991. We briefly explain the formalism of real trees, which yields a neat presentation of the theory and in particular of the relations between discrete Galton-Watson trees and continuous random trees. We then discuss the particular class of self-similar random real trees called stable trees, which generalize the CRT. We review several important results concerning stable...
Sur l'équation stochastique de Tsirelson
Stochastic flows associated to coalescent processes II : stochastic differential equations
Conditioned brownian trees
Un processus qui ressemble au pont brownien
The brownian cactus I. Scaling limits of discrete cactuses
The cactus of a pointed graph is a discrete tree associated with this graph. Similarly, with every pointed geodesic metric space , one can associate an -tree called the continuous cactus of . We prove under general assumptions that the cactus of random planar maps distributed according to Boltzmann weights and conditioned to have a fixed large number of vertices converges in distribution to a limiting space called the Brownian cactus, in the Gromov–Hausdorff sense. Moreover, the Brownian cactus...
A probabilistic approach to the trace at the boundary for solutions of a semilinear parabolic partial differential equation.
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