Benjamin Gess (Universität Bielefeld)

Fluctuations in continuum and conservative SPDEs

Fluctuations are ubiquitous in real world contexts, ranging from thermal fluctuations in physical systems, to algorithmic stochasticity in machine learning, to fluctuations caused by small-scale weather patterns in climate dynamics. A systematic understanding of the interplay of stochasticity and complex dynamical behavior aims to unveil universal properties, irrespectively of the many details of the concrete systems at hand. In this talk, we will identify the class of conservative stochastic partial differential equations (CSPDEs) as universal fluctuating continuum models, and their analysis as a fruitful field for the discovery of new mathematical structures and methods. In particular, we will demonstrate how CSPDEs arise from fluctuating interacting particle systems, and, vice versa, how the analysis of CSPDEs can guide the mathematical insight into the nonequilibrium fluctuations of complex systems.

Leandro Chiarini (Utrecht University)

Scaling limits and fluctuations of discrete stochastic PDEs

In this talk, we will discuss central limit types of results for those discrete approximations of stochastic PDEs driven by random walks either on random environment or with heavy-tails. Furthermore, we will study couplings between the discrete and continuous stochastic PDEs that allow us to find a non-trivial fluctuations around the limiting field. This is based on joint works with Wioletta Ruszel (Utrecht) and Milton Jara (Rio).

Mark Veraar (TU Delft)

Optimal rates for pathwise approximations of solutions to stochastic PDEs

In this talk I will explain some new convergence results for a class of stochastic PDEs. Typical examples for which the results are useful are hyperbolic stochastic PDEs. The main novelties are:

• – the convergence rates are optimal up to a logarithmic factor
• – the convergence is obtained for the whole paths

To prove the results new maximal inequalities for stochastic convolutions were required, which will also be discussed. Several examples will be discussed to illustrate the new phenomena.

The talk is based on joint work with Katharina Klioba.