CRC/TRR 388 project A11
Fluctuations and stochastic dynamics in singular and interacting systems
Project A11 studies how fluctuations and stochastic dynamics interact with singular structures and geometry. Its three work packages address distinct applications but share a common mathematical language based on scaling limits, central limit theorems, large deviations and modified equations.
The project combines foundational analysis with algorithmic questions and contributes to the wider CRC/TRR programme linking rough analysis, stochastic dynamics, geometry and applications under uncertainty.
Work packages
- Interacting-particle fluctuations: fluctuation corrections beyond laws of large numbers for systems with degenerate parabolic behaviour.
- Geometric stochastic-gradient methods: effective equations and stochastic flows for optimization on curved parameter and data spaces.
- Singular SPDE dynamics: long-time evolution and qualitative behaviour for equations beyond classical regularity regimes.
The work packages are deliberately interconnected: particle-system limits inform continuum and learning models, geometric ideas feed into stochastic-flow analysis, and singular-SPDE techniques help describe effective limiting dynamics.
Project facts
| Programme | DFG Collaborative Research Centres CRC/Transregios |
| Parent centre | TRR 388 Rough Analysis, Stochastic Dynamics and Related Fields |
| Subproject | A11 |
| Parent DFG project number | 516748464 |
| Subproject DFG number | 568094990 |
| Period | Since 2025 |
| Project heads | Benjamin Gess and Sebastian Kassing |
SAiS team
Research areas
Official sources
Related publications
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Convergence rate for Fluctuations of mean field interacting diffusion and application to 2D viscous Vortex model and Coulomb potential
For a system of mean field interacting diffusion on $\mathbb{T}^d$, the empirical measure $μ^N$ converges to the solution $μ$ of the Fokker-Planck equation. Refining this mean field limit as a Central Limit Theorem, the fluctuation process $ρ^N_t= \sqrt{N}( μ^N_t -μ_t)$ convergences to…
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Fluctuation behaviour for interacting particle systems with common noise
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…