Ronan Memin's webpage



About me

I am a post doctoral student at IMT in the probability team with Michel Pain. My research focuses on random matrix theory and its interactions with integrable systems. I have completed my PhD thesis under the supervision of Alice Guionnet (ENS Lyon) in September 2023. You can find my CV here.


Contact

You can reach me at ronan.memin[at]math.univ-toulouse.fr. Don't hesitate to contact me for anything! I am open to collaborations.

Research papers

PhD thesis

You can access my PhD thesis Analysis of certain integrable models via random matrix theory here. The key objects at stake are the following:

- discrete space integrable systems, such as the Toda chain, or the Ablowitz-Ladik lattice, whose dynamic can be encoded by the evolution of a Lax pair, which is a pair of N by N matrices.
- the beta ensembles of random matrix theory, which are the law of the spectrum of particular instances of random matrices. The real beta ensemble is the probability measure on R^N given, for any beta > 0 and V going fast enough to infinity, by
Here, we are interested in the high temperature regime, which is the regime where beta is proportional to 1/N.

Motivated by the derivation of a hydrodynamic limit for integrable systems, Herbert Spohn uses a comparison between integrable systems and the beta-ensembles at high temperature. We strenghten the understanding of this link through a large deviations approach for the empirical measure of eigenvalues of the matrices of interest, and through the study of the fluctuations of those measures.






Last update of the website: 11 Nov. 2024