Webpage of Thomas Budzinski

Who am I ?

Since the beginning of 2021, I am a "chargé de recherche" (Junior permanent research position) at the UMPA in the ENS Lyon. My office is MGN1-460. From 2019 to 2020, I was a Postdoctoral Fellow in the probability group of the Mathematics Department at UBC (Vancouver). From 2016 to 2019, I was a teaching assistant at the mathematics department of the ENS Paris. My main research interest is the study of random planar maps. I have completed my PhD about hyperbolic random planar maps in Orsay, under the supervision of Nicolas Curien. Here is my CV.

Research papers

Local limits of random bipartite maps in high genus: the general case, in Electronic Communications in Probability
Distances and isoperimetric inequalities in random triangulations of high genus, with Guillaume Chapuy and Baptiste Louf, preprint [slides] [video by Guillaume]
Maximum Agreement Subtrees and Hölder homeomorphisms between Brownian trees, with Delphin Sénizergues, in Journal de l'École Polytechnique [slides]
The critical Karp-Sipser core of random graphs, with Alice Contat and Nicolas Curien, preprint [video by Alice]
On Cheeger constants of hyperbolic surfaces, with Nicolas Curien and Bram Petri, preprint [slides]
Multi-ended Markovian triangulations and robust convergence to the UIPT, in Annales Henri Lebesgue [slides]
Local limits of bipartite maps with prescribed face degrees in high genus, with Baptiste Louf, in Annals of Probability
Cooperative and stochastic multi-player multi-armed bandits: optimal regret with neither communication nor collisions, with Sébastien Bubeck and Mark Sellke, at COLT 2021
Coordination without communication: optimal regret in two players multi-armed bandits, with Sébastien Bubeck, at COLT 2020 [slides] [video]
Recurrence of the Uniform Infinite Half-Plane Map via duality of resistances, with Thomas Lehéricy, in Annals of Probability [slides] [video]
The diameter of random Belyi surfaces, with Nicolas Curien and Bram Petri, in Algebraic and Geometric Topology
On the minimal diameter of closed hyperbolic surfaces, with Nicolas Curien and Bram Petri, in Duke Mathematical Journal [slides]
Universality for random surfaces in unconstrained genus, with Nicolas Curien and Bram Petri, in Electronic Journal of Combinatorics [slides]
Local limits of uniform triangulations in high genus, with Baptiste Louf, in Inventiones Mathematicae [slides] [video]
Supercritical causal maps: geodesics and simple random walk, in Electronic Journal of Probability [slides]
Infinite geodesics in hyperbolic random triangulations, in Annales de l'Institut Henri Poincaré B
On the mixing time of the flip walk on triangulations of the sphere, in Comptes-rendus mathématiques de l'Académie des Sciences [slides]
The hyperbolic Brownian plane, in Probability Theory and Related Fields [slides]

Here are also my PhD thesis and the slides (in french) of the defense.

Other works (in french)

Un résultat de recherche obtenu grâce à des lycéens, with Giancarlo Lucchini Arteche, in the Gazette des Mathématiciens.
My Master Thesis, under the supervision of Nicolas Curien, about the spatial Markov property of planar maps [slides]
My ENS first year thesis, with Jaouad Mourtada, under the supervision of Harald Helfgott, about the diameter of permutation groups
My TIPE about percolation, and the slides of the talk I gave about the same topic at the Students seminar of lycée Louis-le-Grand.

Nice pictures

This page contains various simulations of random triangulations.

Teaching

This year I give an M2 course on Random walks at the ENS of Lyon. Here are a few references that can be useful to find exercises or to go further.
- First part of the course: Random walks and graphs by Nicolas Curien.
- For more on random trees: Arbres et marches aléatoires by Kortchemski (in french, similar to what we have done in class but goes a bit further and gives more context), Random trees and applications by Le Gall (mostly on scaling limits). See also some nice pictures by Igor Kortchemski.
- Second part: Probability on Trees and Networks by Lyons and Peres (with hints for the exercises in the end), Probability and Geometry on Groups by Pete.
See here for previous years (in french).