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Universität Augsburg
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Universität Augsburg
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Dr. Paul Chleboun
University of Warwick
spricht am
Mittwoch, 10. Juli 2024
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| We discuss the Inclusion Process, which is a stochastic particle system known to exhibit condensation and metastable dynamics in various regimes when the diffusivity parameter tends to zero. We consider the process on the complete graph in the thermodynamic (at fixed particle density), focusing on the dynamics of the empirical mass distribution. By describing particle configurations in terms of size-biased and appropriately scaled empirical measures of the mass distribution, we establish convergence to a limiting measure-valued Markov process. When the diffusivity vanishes inversely with the system size, the derived scaling limit is equivalent to the well-known Poisson-Dirichlet diffusion. Moreover, our size-biased approach provides a robust description of the dynamics, which covers all scaling regimes of the system parameters and yielding a natural extension of the Poisson-Dirichlet diffusion to infinite mutation rate. This is joint work with Simon Gabriel (Münster) and Stefan Grosskinsky (Augsburg). |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Stefan Großkinsky |