Quantitative convergence guarantees for the mean-field dispersion process
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914000104587264 |
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| author | Cao, Fei Yang, Jincheng |
| author_facet | Cao, Fei Yang, Jincheng |
| contents | 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 $μ> 0$), we establish various quantitative long-time convergence guarantees toward the global equilibrium (depending on the sign of $μ- 1$), 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05043 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative convergence guarantees for the mean-field dispersion process Cao, Fei Yang, Jincheng Probability Classical Analysis and ODEs 82C22, 82C31, 35Q91, 91B80 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 $μ> 0$), we establish various quantitative long-time convergence guarantees toward the global equilibrium (depending on the sign of $μ- 1$), 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. |
| title | Quantitative convergence guarantees for the mean-field dispersion process |
| topic | Probability Classical Analysis and ODEs 82C22, 82C31, 35Q91, 91B80 |
| url | https://arxiv.org/abs/2406.05043 |