Ronan Memin's webpage

About me

Since October 2025, I am part of the Statistical Physics and Mathematics program as a post doctoral researcher at DMA (ENS, Paris). Before that I was at IMT (Toulouse) as a postdoc with Michel Pain, and I have completed my PhD thesis under the supervision of Alice Guionnet (ENS Lyon) in September 2023.

My research focuses on random matrix theory and its interactions with statistical physics and integrable systems ; and more generally, I am interested in the study of random matrices through large deviations for the spectrum/the largest eigenvalue, fluctuations/local statistics of the spectrum.

You can find my CV here.

Contact

You can reach me at ronan.memin[at]ens.fr.

Research papers

• Large deviations at the edge for 1D gases and tridiagonal random matrices at high temperature, with Charlie Dworaczek Guera [arXiv preprint]
• CLT for real beta-ensembles at high temperature, with Charlie Dworaczek Guera [Electronic Journal of Probability, link]
• CLT for beta ensembles at high temperature, and for integrable systems : a transfer operator approach, with Guido Mazzuca [Annales de l'Institut Henri Poincaré, link]
• Large deviations for the Ablowitz-Ladik lattice, and the Schur flow, with Guido Mazzuca [Electronic Journal of Probability, link]
• Large deviations for generalized Gibbs ensembles of the classical Toda chain, with Alice Guionnet [Electronic Journal of Probability, link]

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 recently used 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: 06 Oct. 2025