Periodicity and longtime diffusion for mean field systems in $\mathbb{R}^d$

Eric Luçon; Christophe Poquet

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arXiv · 2107.02473

Periodicity and longtime diffusion for mean field systems in $\mathbb{R}^d$

Eric Luçon·Christophe Poquet

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Abstract

We study in this paper the longtime behavior of some large but finite populations of interacting stochastic differential equations whose (infinite population) limit Fokker-Planck PDE admits a stable periodic solution. We show that the empirical measure for the population of size $N$ stays close to the periodic solution, but with a random dephasing at the timescale $Nt$ that converges weakly to a Brownian motion with constant drift.

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Eric Luçon, Christophe Poquet. 2021-07-06. Periodicity and longtime diffusion for mean field systems in $\mathbb{R}^d$. https://arxiv.org/abs/2107.02473

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