20.04.2026 16:30 Piotr Dyszewski:
The Largest Fragment in Self-Similar Fragmentation Processes (Parkring 11, 85748 Garching-Hochbrück)
In this talk, we study a self-similar fragmentation process with index a>0, modeling the evolution of particles that break into smaller fragments over time. In this setting, the fragmentation rate of a particle of size u is proportional to u^a. We present asymptotic results describing the size of the largest fragment in the system. In particular, we establish a precise connection between the asymptotic behavior of the largest fragment and that of the so-called dislocation measure, which governs the underlying fragmentation mechanism.
This is based on joint work with Samuel G. G. Johnston, Sandra Palau, and Joscha Prochno: https://arxiv.org/pdf/2409.11795