# 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 here
my CV (last update: 27 March 2023).

## 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

- CLT for real beta-ensembles at high temperature, with Charlie Dworaczek Guera [preprint, arXiv:1310.7835]
- CLT for beta ensembles at high temperature, and for integrable systems
: a transfer operator approach, with Guido Mazzuca [Annales de l'Institut Henri
PoincarĂ©, 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 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: 15 Oct. 2024