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arXiv · 2406.05043

Quantitative convergence guarantees for the mean-field dispersion process

Fei Cao·Jincheng Yang
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Abstract

We study the discrete Fokker-Planck equation associated with the mean-field dynamics of a particle system called the dispersion process. For different regimes of the average number of particles per site (denoted by $\mu > 0$), we establish various quantitative long-time convergence guarantees toward the global equilibrium (depending on the sign of $\mu - 1$), which is also confirmed by numerical simulations. The main novelty/contribution of this manuscript lies in the careful and tricky analysis of a nonlinear Volterra-type integral equation satisfied by a key auxiliary function.

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Fei Cao, Jincheng Yang. 2024-06-07. Quantitative convergence guarantees for the mean-field dispersion process. https://doi.org/10.3934/dcds.2025126

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