Short research statement
I am mainly interested in mean-field kinetic theory. Namely, I try to describe the statistical behavior of numerous particles interacting through a long-range potential. The average behavior of such a system is described by a Vlasov-like partial differential equation. Justifying this behavior boils down to proving a law of large numbers (or a "mean-field limit") for the particle system.
In my PhD thesis [T], I worked with the "modulated energy" method introduced by Duerinckx and Serfaty, which is particularly convenient to prove mean-field limits of systems of particles with singular interactions coming from many physical backgrounds. I adapted this method to two different systems related to fluid dynamics:
- In [1] I gave a derivation of a two-dimensional gyrokinetic spray model introduced by Moussa and Sueur. This model describes the evolution of a continuous density of solid particles immersed in an incompressible fluid.
- In [2] I established the mean-field limit derivation of the lake equations from a model of point vortices introduced by Richardson.
In my current position, I am interested in the long-time behavior and fluctuations of particle systems. With Armand Bernou and Mitia Duerinckx, we studied in [4] the
creation of chaos phenomenon for interacting Brownian particles: starting initially from an arbitrary exchangeable N-particle distribution, whe show that the mean-field approximation holds with an accuracy O(
N-1), up to an error due solely to initial pair correlations, which is damped exponentially over time. This is complemented by corresponding results on higher-order creation of chaos in the form of higher-order correlation estimates.
Besides kinetic theory, I worked on spectral theory with Christophe Lacave and Catherine Sulem. We studied in [3] the spectrum of the Dirichlet-Neumann operator that characterizes the propagation of linear water waves. We showed that when the bottom is small and periodic, some conditions on its Fourier coefficients ensure the apparition of small gaps in the spectrum of the Dirichlet-Neumann operator.
Preprints
Publications
The preprints of these publications can be found on
arXiv and on
Hal.
PhD thesis