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Universität Augsburg
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Universität Augsburg
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Max Grübmeyer
Universität Augsburg
spricht am
Freitag, 17. Juli 2026
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10:00 Uhr
im
Raum 3008 (L1)
über das Thema:
| Abstract: |
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In this talk we will give an overview of two different interacting particle systems and derive their mean field limit.
First we will handle the case of non-interacting Brownian motion in $\mathbb{R}^d$ given by the stochastic differential equations $X_i(t) = X_i(0) +
\sqrt2 B_i(t)$. We will show that the empirical measure converges to a deterministic one and that that limiting measure solves the heat equation in a weak sense.
Afterwards, we will consider a Brownian particle system subject to a mean field drift of the form $dX_i(t) = b(X_i(t), \mu_t^N)dt + \sqrt2dB_i(t)$. We will once again show that this system's empirical measure converges to a deterministic object and that the limit solves a nonlinear Fokker-Planck type partial differential equation of the form $\partial_t\rho = - abla \cdot (b(x, \rho)\rho) + \Delta \rho$. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Chengcheng Ling |