Date/heure
6 mai 2026
16:45 - 17:45
Oratrice ou orateur
Louis Chataîgnier (Université de Toulouse)
Catégorie d'évènement Séminaire des doctorants
Résumé
We consider branching Brownian motion (BBM), a random process
that describes the evolution of a particle population, reproducing and
moving independently. Beyond obvious biological motivations and its link
with the F-KPP equation, BBM can be seen as a toy model for spin
glasses, such as the Sherrington-Kirkpatrick model. In this perspective,
we will introduce the Gibbs measures of BBM. We will study some of their
properties, including their connection with the so-called additive
martingales. We will also study the maximal particle of BBM (or, from
the perspective of statistical physics, the ground state of the system).
A new martingale then appears, that is, the derivative martingale. If
time allows, we will briefly present an ongoing work with Gabriel Flath and Julien Berestycki,
in which we obtain an almost sure path localization of the derivative
martingale.