Publications
Preprints (submitted):
Generalized Langevin and Nosé-Hoover processes absorbed at the boundary of a metastable domain. With A. Guillin, D. Lu, and L. Wu. Preprint.
Central Limit Theorem for Bayesian neural network trained with Variational Inference. With A. Descours, A. Guillin, T. Huix, M. Michel, and E. Moulines. Preprint.
Eyring-Kramers exit rates for the overdamped Langevin dynamics: the case with saddle points on the boundary. With T. Lelièvre and D. Le Peutrec, 2022. Preprint.
Accepted or published papers:
Exit time and principal eigenvalue of non-reversible elliptic diffusions. With D. Le Peutrec and L. Michel, 2023. Accepted in Communications in Mathematical Physics.
Quasi-stationary distribution for strongly Feller Markov processes by Lyapunov functions and applications to hypoelliptic Hamiltonian systems. With A. Guillin and L. Wu. Accepted in the Journal of the European Mathematical Society, 2020.
Law of large numbers and central limit theorem for wide two-layer neural networks: the mini-batch and noisy case. With A. Descours, A. Guillin, and M. Michel. Accepted in the Journal of Machine Learning Research, 2022.
Eyring-Kramers type formulas for some piecewise deterministic Markov processes. With D. Le Peutrec and L. Michel. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2022. To appear.
Law of Large Numbers for Bayesian two-layer Neural Network trained with Variational Inference. With A. Descours, A. Guillin, T. Huix, M. Michel, and E. Moulines. Conference on Learning Theory (COLT), 2023.
Quasi-stationary distribution for Hamiltonian dynamics with singular potentials. With A. Guillin and L. Wu. 2021. Probability Theory and Related Fields, 2022.
The exit of a metastable state : concentration of the exit point distribution on the low energy saddle points, part 2. With T. Lelièvre and D. Le Peutrec. Stochastics and Partial Differential Equations: Analysis and Computations, 2021.
Mean exit time for the overdamped Langevin process: the case with critical points on the boundary. Communications in Partial Differential Equations, 2021. (Erratum)
Eigenvalues of the Witten Laplacian with Dirichlet boundary conditions: the case with critical points on the boundary. With D. Le Peutrec. Analysis & PDE, 2021.
Low lying eigenvalues and convergence to the equilibrium of some Piecewise Deterministic Markov Processes generators in the small temperature regime. With A. Guillin. Annales Henri Poincaré, A Journal of Theoretical and Mathematical Physics, 2020.
Repartition of the quasi-stationary distribution and first exit point density for a double-well potential. With D. Le Peutrec. SIAM Journal on Mathematical Analysis, 2020.
The exit of a metastable state : concentration of the exit point distribution on the low energy saddle points, part 1. With G. Di Gesù, T. Lelièvre, and D. Le Peutrec. Journal de Mathématiques Pures et Appliquées, 2020.
Note: longer version from arXiv: here.Sharp estimate of the mean exit time of a bounded domain in the zero white noise limit. Markov Processes And Related Fields, 2020.
Sharp asymptotics of the first exit point density. With G. Di Gesù, T. Lelièvre, and D. Le Peutrec. Annals of PDE, 2019.
Jump Markov models and transition state theory : the quasi-stationary distribution approach. With G. Di Gesù, T. Lelièvre, and D. Le Peutrec. Faraday Discussions, 2016.
Conference papers (with reviews):
Recent advances in the long-time analysis of killed degenerate processes and their particle approximation. With B. Cloez, L. Journel, P. Monmarché, et M. Ramil. ESAIM: Proceedings and Surveys, 2023.
Exit event from a metastable state and Eyring-Kramers law for the overdamped Langevin dynamics. With T. Lelièvre and D. Le Peutrec. Stochastic Dynamics out of Equilibrium, G. Giacomin, S. Olla, E. Saada, H. Spohn and G. Stoltz (Eds), Springer Proceedings in Mathematics and Statistics, 2018.