Henrik Weber

Scaling limits of interacting particle systems via SPDE methods

2nd February 2026
The derivation of hydrodynamic and fluctuation limits for interacting particle systems is a classical theme in probability theory and mathematical physics.

In this talk, I will describe a new approach to such scaling limits inspired by modern techniques for singular stochastic partial differential equations, in particular the theory of regularity structures. As a concrete case study, I will discuss the weakly asymmetric simple exclusion process on a circle and its convergence, under diffusive scaling, to the Kardar–Parisi–Zhang (KPZ) equation. This convergence is a classical result, first established by Bertini and Giacomin in the 1990s.

Traditionally, the proof relies on the non-linear Gärtner (Cole–Hopf) transform, which linearises the problem at the discrete level. I will explain how one can instead analyse the particle system directly, without relying on such integrable structures, by adapting SPDE methods to a discrete, jump-driven setting. This leads to a flexible and robust framework that is expected to extend to a broad class of interacting particle systems.

Karsten Matthies

Timescales for the invariance principle of the random Lorentz gas

9th February 2026
We study the timescale T(r) of the invariance principle for a Lorentz gas with particle size r and improve results by obtained by Lutsko and Toth (2020). The work includes improved geometric recollision estimates and a discussion of the coupling of stochastic processes introduced in the original result. Joint work with Raphael Winter.

Irene Ayuso Ventura

Imry–Ma phenomenon for the hard-core model on ℤ²

16th February 2026
I will present recent joint work with Leandro Chiarini, Tyler Helmuth, and Ellen Powell on the hard-core model on ℤ², a model of independent sets on the square lattice. We show that under weak random disorder, this model has no phase transition in two dimensions. This behavior is known as the Imry–Ma phenomenon, whose most classical example is the random-field Ising model. Our proof is inspired by the Aizenman–Wehr argument for the random-field Ising model, but relies on spatial symmetries rather than internal spin symmetries.