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Universität Augsburg
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Universität Augsburg
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Elena Magnanini
WIAS Berlin
spricht am
Mittwoch, 14. Januar 2026
um
14:30 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| We present recent advances on a stochastic coagulation particle system (Marcus-Lushnikov process) , in which pairs of particles coagulate after independent exponential waiting times. The model can be regarded as a microscopic counterpart of Smoluchowski’s coagulation equation introduced in 1917. We focus on a spatial extension of the process, where particles are characterized by both a mass and a spatial position, and where coagulation rates depend on these attributes through a positive symmetric kernel. When two particles coagulate, their masses are added, while the spatial position of the resulting particle is updated according to a prescribed spatial rule. For suitable choices of the coagulation kernel, the system exhibits a gelation-type phase transition, characterized by the formation, in finite time, of particles with macroscopic mass. We derive two sufficient criteria ensuring the occurrence of gelation; as a corollary, one of these criteria resolves an open conjecture in the classical non-spatial setting. In addition, we prove a law of large numbers establishing the convergence of the appropriately rescaled stochastic process towards a spatial Flory equation. Finally, we discuss several open questions and directions for ongoing research within this framework. This talk is based on joint works with L. Andreis, and T. Iyer. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Markus Heydenreich |