Webpage of Armand Riera

ARMAND RIERA

Associate Professor (MCF) at Sorbonne université | Research Team : Stochastic analysis.

My research interests lie primarily on the field of 2-dimensional random geometry, specifically in the study of scaling limits of models of random planar maps. These limit objects are used to construct natural measures on certain classes of metric spaces and allow to define random surfaces. This theory, commonly referred to as Brownian Geometry, is an interdisciplinary field that combines elements of combinatorics, physics, and probability theory.

To investigate these structures, I use a range of stochastic processes including growth-fragmentation processes, branching processes, and superprocesses.

Research

Spatial Markov property in Brownian disks | with Jean-François Le Gall (To appear in Ann. Inst. Henri Poincaré Probab. Stat. 43 pages)
Surfaces Browniennes | Disclosure article in French (To appear in Matapli, 18 pages)
The structure of the local time of Markov processes indexed by Levy trees | with Alejandro Rosales-Ortiz (To appear in Probab. Th. Rel. Fields, 99 pages)
Isoperimetric inequalities in the Brownian plane | (Ann. Probab. 50 (2022), 42 pages)
Spine representations for non-compact models of random geometry | with Jean-François Le Gall (Probab. Th. Rel. Fields 181 (2021), 74 pages)
Some explicit distributions for Brownian motion indexed by the Brownian tree | with Jean-François Le Gall (Markov Processes Relat. Fields 26 (2020), 27 pages, Special issue)
Growth-fragmentation processes in Brownian motion indexed by the Brownian tree | with Jean-François Le Gall (Ann. Probab. 48 (2020), 42 pages)
PhD Thesis: Brownian Geometry. Under the supervision of Jean-François Le Gall. (This thesis was awarded the Prix de thèse Jacques Neveu 2022 de la SMAI.)