Many macroscopic laws arise from large systems of randomly interacting particles far from equilibrium.
Published · Stochastics and Partial Differential Equations: Analysis and Computations (2026). We consider the asymptotic behaviour of the fluctuation process for large stochastic systems of interacting particles driven by both idiosyncratic and common noise with an interaction kernel \(k \in L^2(\R^d) \cap L^\infty(\R^d)\). Our analysis relies on uniform relative entropy estimates and Kolmogorov’s…
Published · Stochastics and partial differential equations : analysis and computations, 14 (2026) 1, pp. 350-388. The purpose of this paper is to establish a well-posedness theory for conservative stochastic partial differential equations on the whole space. This class of stochastic PDEs arises in fluctuating hydrodynamics, and includes…
A quantitative central limit theorem for the simple symmetric exclusion process (SSEP) on a $d$-dimensional discrete torus is proven. The argument is based on a comparison of the generators of the density fluctuation field of the SSEP and the generalized Ornstein-Uhlenbeck process,…
Published · SIAM Journal on Mathematical Analysis 57(3), 3071–3109 (2025). We derive quantitative estimates proving the conditional propagation of chaos for large stochastic systems of interacting particles subject to both idiosyncratic and common noise. We obtain explicit bounds on the relative entropy…
Published · Stochastic processes and their applications, 193 (2026), p. 104847. Higher order fluctuation expansions for stochastic heat equations (SHE) with nonlinear, non-conservative and conservative noise are obtained. These Edgeworth-type expansions describe the asymptotic behavior of solutions in suitable joint scaling regimes of…
Published · SIAM journal on control and optimization, 62 (2024) 6, pp. 3288-3314. We give quantitative estimates for the rate of convergence of Riemannian stochastic gradient descent (RSGD) to Riemannian gradient flow and to a diffusion process, the so-called Riemannian stochastic modified flow (RSMF). Using…
Accepted / forthcoming · Annals of Applied Probability. The dynamical large deviations principle for the three-dimensional incompressible Landau-Lifschitz-Navier-Stokes equations is shown, in the joint scaling regime of vanishing noise intensity and correlation length. This proves the consistency of the large…
Published · Communications on pure and applied mathematics, 78 (2025) 9, pp. 1609-1655. The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied…
Published · Journal of machine learning research, 25 (2024) 30, pp. 1-27. We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called…
Published · Probability theory and related fields, 192 (2025) 3/4, pp. 1447-1515. The convergence of stochastic interacting particle systems in the mean-field limit to solutions of conservative stochastic partial differential equations is established, with optimal rate of convergence. As a second main result, a…
