Collaborators: Marc Arnaudon (Bordeaux), Xin Chen (Shanghai Jiaotong University), C. Roberto (Paris), David Elworthy (Warwick), Johann Gehringer, Luca Gerolla, Z. Gozlan( Delaware), Martin Hairer (EPFL/ICL), M. Madiman (Nanterre), Benedikt Petico, Fabien Panloup (Angers), Steven Rosenberg (Boston), P.-M. Samson (Gustave Eiffel), Julian Sieber, Bo Wu (Fu Dan University), Kexing Ying (EPFL), Marc Yor.
Preprints.
Coarse extrinsic curvature of Riemannian submanifolds, To appear in the European Journal of Mathematical Society.
Scaling limit of the KPZ equation with non-integrable spatial correlations (2024)
Fluctuations of stochastic PDEs with long-range correlations, to appear: To appear in the Annals of Applied Probability.
Homogenization with fractional random fields, arXiv:1911.12600 ( 2019)
Recent Publications.
Generating diffusions with fractional Brownian motion, Communications in Mathematical Physics, 396, 91-141 (2022)
Logarithmic heat kernel estimates without curvature restrictions, Annals of Probability, (2023)
Slow-fast systems with fractional environment and dynamics, Annals of Applied Probability (2022)
Functional limit theorems for the fractional Ornstein-Uhlenbeck process, Journal of Theoretical Probability (2022)
On the (Non-)Stationary Density of Fractional-Driven Stochastic Differential Equations (2023)
Log-Hessian and Deviation Bounds for Markov Semi-Groups, and Regularization Effect in L1 (2023) In Potential Analysis
Functional Limit Theorems for Volterra Processes and Applications to Homogenization, In Nonlinearity (2022)
Slow-Fast Systems with Fractional Environment and Dynamics In Annals of Applied Probability (2022)
Mild Stochastic Sewing Lemma, SPDE in Random Environment, and Fractional Averaging, Best paper 2022 Award in Stochastic and Dynamics.
Multi-scale on manifolds.
Averaging Principle for a completely integrable stochastic Hamiltonian system (2008) Nonlinearity 21, Random perturbation to the geodesic equation, Annals of Probability (2016)
Homogenisation on homogeneous spaces, Journal of Mathematical Society of Japan (2018)
Limits of random differential equations on manifolds, Probability Theory and Related Fields
Selected Publications.
Geometric stochastic analysis on path spaces, International Congress of Mathematicians 2006.
Averaging dynamics driven by fractional Brownian motion, Annals of Probability, (2020)
Formulae for the derivatives of heat semigroups, Journal of Functional Analysis (1994)
Strong p-completeness of stochastic differential equations and the existence of smooth flows on noncompact manifolds, Probability Theory and Related Field (1994)
The importance of strictly local martingales; applications to radial Ornstein-Uhlenbeck processes, Probability Theory and Related Fields (1997)
Barycenters of measures transported by stochastic flows, The Annals of Probability (2005)
Stochastic differential equations on noncompact manifolds: moment stability and its topological consequences, Probability Theory and Related Fields (1994)
On extensions of Meyers theorem (1995) Bulletin of London Mathematical Society