Recent Trends in Stochastic Partial Differential Equations: Gaussian Fluctuations in the 4D Anderson model
Presenter
November 18, 2025
Keywords:
- stochastic partial differential equations
- regularity structures
- paracontrolled calculus
- nonlinear dispersive equations
- Gibbs measures
- homogenization
- stochastic fluid dynamics
- quantum field theory
MSC:
- 60H15 - Stochastic partial differential equations (aspects of stochastic analysis)
Abstract
We perform a perturbative analysis of the scaling invariant 4D Anderson model, with the aim of establishing Gaussian fluctuations in the transition from delocalised to localised states on finite volume. We prove Gaussian fluctuations in a weak coupling regime, in a perturbative sense, as well as the appearance of a phase transition reminiscent of the 2D stochastic heat flow. Joint work with Simon Gabriel.