Math Calendar
Monday, July 13, 2026
09:00-10:00
MINN-0.09
MSc thesis presentation
Iddo Bruijn - The Role of Self-Interaction in the Mean-Field Limit and Critical Fluctuations of an Interacting Particle Model
see description
Supervisor: Dr. Alexandra Holzinger
Secondexaminer: Prof. Dr.Wioletta Ruszel.
Abstract: Modeling interacting particle systems is a fundamental task in many areas of science. Systems of stochastic differential equations provide an accurate microscopic model but arecomputationally expensive for large particle numbers. A deterministic partial differential equation instead can model the density accurately on a macroscopic scale. The mean-field limit connects the two descriptions, and the associated fluctuation process yields a stochastic correction to the macroscopic PDE.
In this work, the role of the self-interaction within a mean-field model is examined. Mean-field and fluctuation-process limits are proven under general assumptions on the self-interaction. At criticality, where the limiting fluctuation process becomes unstable, a rescaled fluctuation limit is derived. These results are illustrated using two specific self-interactions, both theoretically and through numerical simulations.Thursday, July 16, 2026
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Thursday, January 7, 2027