54th Probability Summer School
Saint-Flour (France), June 29th – July 11th 2026
Founded in 1971, this school is organised every year by the Laboratoire de Mathématiques Blaise Pascal (UMR 6620). It is supported by Clermont Auvergne University and C.N.R.S. It is intended for PhD students, teachers and researchers who are interested in probability theory, statistics, and in applications of these techniques.
The school has three main goals:
- to provide, in high level courses, a comprehensive study of a field in probability theory or statistics;
- to enable the participants to explain their work in lectures;
- to facilitate exchanges between the participants.
The lecturers are chosen by the Scientific Board of the school.
Lectures are published by Springer in the Lecture Notes series and videorecorded on YouTube.
Lectures 2026
François DELARUE (Université Côte d'Azur), Mean-Field Systems: Randomization and Control.
This course aims to cover two topics related to the analysis of large systems of weakly interacting particles and, ultimately, to bring them together. The common foundation of the two directions that will be pursued is the theory of diffusive mean-field models, or McKean–Vlasov stochastic differential equations. We will study how optimization interacts with the mean-field limit, and how randomization of the limiting dynamics yields additional exploration properties of the space of probability measures. Direction (i) is connected to the theory of mean-field games and mean-field control; direction (ii) is related to the notion of Wasserstein diffusion, with a link to the Dean–Kawasaki equation.
Nina HOLDEN (Courant Institute of Mathematical Sciences at New York University), Scaling limits of random planar maps.
Planar maps are graphs embedded in the sphere such that no two edges cross. In this course we will present scaling limit results for random planar maps, focusing on convergence under conformal embedding. The limiting surface is a highly fractal surface called a Liouville quantum gravity (LQG) surface, with origins in string theory and conformal field theory.
Thomas M. HUTCHCROFT (California Institute of Technology), Percolation on finite transitive graphs.
In Bernoulli bond percolation, each edge of a graph is either deleted or retained independently at random. This course examines the qualitative properties of the giant component for percolation on large finite transitive graphs, including a full proof of a recent uniqueness result for the supercritical regime in essentially all large finite transitive graphs.
Practical information
The school takes place at the Hôtel-Restaurant Ancien Grand Séminaire.
The Hôtel-Restaurant Ancien Grand Séminaire (an ancient Roman Catholic Seminary) dates from the 18th century. It has a shaded yard and a car park.
Please read the information about the school.
Registrations for the 2026 St Flour summer School are now closed.
Previous schools
The first Saint-Flour summer schools, by P.L. Hennequin (in French)
Information
École d'été de Probabilités de Saint-Flour
LMBP
Université Clermont Auvergne — CNRS
Campus Universitaire des Cézeaux
3, place Mail Vasarely
TSA 60026 — CS 60026
63178 Aubière Cedex
Organizing Committee:
- Cédric Barrel (IT support staff, UCA),
- Hacene Djellout,
- Arnaud Guillin,
- Boris Nectoux,
- Valérie Sourlier (administrative manager, UCA)
e-mail: Afficher l'adresse email