Plenary session 1

Monday, 7/14, 9:00-12:00, Congress Centre

On rates in the central limit theorem for a class of convex costs

Florence Merlevède (Université Gustave Eiffel)

In this talk, we will shall give estimates not only of the usual quadratic transportation cost, but also of a broader class of convex costs between normalized partial sums associated with real-valued random variables and their limiting Gaussian distribution. For the quadratic transport cost, estimates will be given in terms of weak-dependent coefficients that are well suited to a large class of dependent sequences. This class includes irreducible Markov chains, dynamical systems generated by intermittent maps or strong mixing sequences. We will also present very recent results in the independent framework for a broader class of convex costs that includes quadratic cost as a special case but also certain logarithmic costs such as \(|x| \ln (1+ |x|)\). This talk is based on joint works with J. Dedecker and E. Rio.

Quantitative approximation of Dean-Kawasaki and KPZ equations

Nicolas Perkowski (FU Berlin)

Effective descriptions of large systems of interacting particles often lead to singular stochastic PDEs, equations with noise so rough that classical theory breaks down. Two emblematic cases are the Dean-Kawasaki equation, modeling mesoscopic density fluctuations in mean-field particle systems, and the KPZ/Burgers equation, describing interface growth fluctuations. In this talk I quantify the weak approximation error when replacing the true dynamics with these effective SPDEs. The key ingredients are new regularity estimates for the associated infinite-dimensional Kolmogorov equations, which allow a direct comparison of the infinitesimal generators. Based on joint work with Ana Djurdjevac, Lukas Gräfner, Helena Kremp and Xiaohao Ji.