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En son coeur, c'est un cours d'analyse fonctionnelle pour les physiciens et traite les bases de théorie de mesure, des espaces des fonctions et opérateurs linéaires.
This is a theoretical course about probability in high dimensions. We will look at some mathematical phenomena appearing as the number of random variables grows large - e.g. concentration of measure o
Le cours est une introduction à la théorie des probabilités. Le but sera d'introduire le formalisme moderne (basé sur la notion de mesure), de lier celui-ci à l'aspect "intuitif" des probabilités mais
We prove that the set of-y-thick points of a planar Gaussian free field (GFF) with Dirichlet boundary conditions is a.s. totally disconnected for all-y =6 0. Our proof relies on the coupling between a GFF and the nested CLE4. In particular, we show that th ...
Consider CLE4 in the unit disk, and let l be the loop of the CLE4 surrounding the origin. Schramm, Sheffield and Wilson determined the law of the conformal radius seen from the origin of the domain surrounded by l. We complement their result by determining ...
INST MATHEMATICAL STATISTICS-IMS2022
We prove that under certain mild moment and continuity assumptions, the d-dimensional continuum Gaussian free field is the only stochastic process satisfying the usual domain Markov property and a scaling assumption. Our proof is based on a decomposition o ...