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.

Kirstin Strokorb

Graphical models for infinite measures with applications to extremes and Lévy processes

23rd February 2026
Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure on the punctured Euclidean space that explodes at the origin. The importance of such measures stems from their connection to infinitely divisible and max-infinitely divisible distributions, where they appear as Lévy measures and exponent measures, respectively. We characterize independence and conditional independence for such measures in various ways through kernels and factorization of a modified density, including a Hammersley-Clifford type theorem for undirected graphical models. As opposed to the classical conditional independence, our notion is intimately connected to the support of the measure. Structural max-linear models turn out to form a Bayesian network with respect to our new form of conditional independence. Our general theory unifies and extends recent approaches to graphical modeling in the fields of extreme value analysis and Lévy processes.

This talk is based on joint work: S. Engelke, J. Ivanovs, and K. Strokorb. Graphical models for infinite measures with applications to extremes. Ann. Appl. Probab. 35(5): 3490-3542 (October 2025). DOI: 10.1214/25-AAP2201

Joost Jorritsma

The critical percolation window in uniformly grown random graphs

2nd March 2026
We study graphs in which vertices 1,...,n arrive sequentially, and in which vertex j connects independently to earlier vertices with probability β/j. Bollobás, Janson, and Riordan (‘05) proved that the phase transition in β beyond which a giant component appears is of infinite order, in sharp contrast to the classical mean-field transition in Erdős–Rényi random graphs.

In this talk we determine the asymptotic order of the largest component at the critical value β_c. Moreover, for sequences β_n → β_c, we describe the critical window and uncover several surprising features, including a secondary phase transition and bounded susceptibility (average component size) throughout the window.

The proofs rely on a coupling between a component exploration process and a branching random walk with two killing barriers.

Joint work with Pascal Maillard and Peter Mörters.