Self-similar Markov trees
Labelled continuum trees designed to encode genealogies together with evolving local sizes. They extend classical fragmentation-type structures by allowing both growth and splitting.
Related publications: [1,4].
Labelled continuum trees designed to encode genealogies together with evolving local sizes. They extend classical fragmentation-type structures by allowing both growth and splitting.
Related publications: [1,4].
Scaling limits of random planar maps, Brownian geometry, spatial Markov properties and metric explorations of random surfaces.
Related publications: [5,6,8,9].
Stable carpets and stable gaskets: random compact metric spaces with macroscopic holes arising from random planar maps with large faces.
Related publications: [2].
Excursion theory, local times, growth-fragmentation phenomena and branching structures indexed by random trees.
Related publications: [3,7,10,11].
Below are selected works. A complete publication list is available on the publications page and in my CV.
With Nicolas Curien and Grégory Miermont — to appear, 186 pages.
We prove convergence of large Boltzmann stable planar maps to a one-parameter family of random compact metric spaces with macroscopic holes.
With Alejandro Rosales-Ortiz — Proceedings of the London Mathematical Society, 2026, 83 pages.
We develop an excursion theory for Markov processes indexed by Lévy trees and describe the genealogy of excursions through a tree coded by local time.
With Jean Bertoin and Nicolas Curien — IMS Monographs, 2026, 336 pages.
We introduce self-similar Markov trees, establish first invariance principles, and show how they arise in a range of random tree and map models.
With Jean-François Le Gall — Probability Theory and Related Fields, 2025, 43 pages.
We establish a spatial Markov property for the Brownian half-plane and analyse hulls centered at boundary points.
With Alejandro Rosales-Ortiz — Probability Theory and Related Fields 189, 2024, 99 pages.
We construct and study local times for Markov processes indexed by Lévy trees and identify the tree structure encoded by their level sets.
Annals of Probability 50, 2022, 42 pages.
We establish sharp isoperimetric bounds for the Brownian plane using spatial Markov properties and the geometry of separating cycles.
Surfaces Browniennes, a French popular-science article written for the Jacques Neveu Prize, Matapli 130 (2023), 18 pages.
Report on The scaling limit of planar maps with large faces, Oberwolfach Reports (2025), 5 pages.
Course 2025-2026: Statistiques des processus, M1 ISUP. Géométrie plainaire discrète aléatoire, M2 Sorbonne Probabilités & Modèles Aléatoires. Théorie de la mesure et Probabilités, L3 Sorbonne. Probabilités approfondies, TD M1 Sorbonne.
Jury for French competitive exams: ENS oral mathematics Ulm 2025 and ENS oral TIPE 2024.
AMSS mini-course: Brownian Geometry and Metric Explorations (8 lectures), Slides course 1/2 , Slides course 3/4 , Slides course 5/6 , Slides course 7/8 ; Exercices GH-distance and BDG bijection .
Exercise sessions: Random Surfaces, Saint-Flour 2019; Self-Similar Markov Branching Trees, Mexico 2022.
Master thesis M2: Étude des limites de permutations aléatoires et application aux permutations séparables.