The spring school organized by the MEGA research group brings together PhD students and postdocs for a week, focusing on topics related to random matrices and random graphs. The 2024 edition will take place in Fréjus (France) - CNRS, 2754 rue Henry Giraud, 83600 FREJUS, from March 25th to March 29th. While the number of participants is limited, we encourage everyone interested to apply.

The classes will begin on Tuesday 26th of March in the morning. It is possible (and recommended) to arrive on Monday 25th.

Three mini-courses will be conducted by Laure Dumaz and Thomas Leblé, and participants will be encouraged to present talks.

The research group intends to support the participation of approximately fifteen individuals (accomodation and food).

Please feel free to reach out to the organizers with any questions.

Organizers:

- Charlie DWORACZEK GUERA charlie.dworaczek(at)ens-lyon.fr

- Martin ROUAULT martin.rouault(at)univ-lille.fr

Programme:

Thomas Leblé's mini-course:

Statistical physics perspective" for the Sine-β process

The Sine-beta process emerges as the limit of the eigenvalues of a "beta-ensemble" - which includes the three classical Gaussian ensembles of random Hermitian matrices - seen at the microscopic scale in the bulk. It is a family of point processes on the real line, indexed by the parameter beta. Coincidentally, the distribution of these eigenvalues can be interpreted as the Gibbs measure of a statistical physics system called the "log-gas". This observation, dating back to Dyson, paves the way for a "physical" approach to their behavior.
The aim of this mini-course is to present its main features, both at the macroscopic scale (which has been known for quite some time) and microscopic scale (particularly for the study of Sine-beta, which is more recent).

Laure Dumaz's mini-course:

Random operators at the limit of random matrices