Quantitative convergence guarantees for the mean-field dispersion process
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| Title: | Quantitative convergence guarantees for the mean-field dispersion process |
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| Authors: | Cao, Fei, Yang, Jincheng |
| Source: | Discrete and Continuous Dynamical Systems. 47:487-518 |
| Publication Status: | Preprint |
| Publisher Information: | American Institute of Mathematical Sciences (AIMS), 2026. |
| Publication Year: | 2026 |
| Subject Terms: | Classical Analysis and ODEs, Probability (math.PR), Classical Analysis and ODEs (math.CA), FOS: Mathematics, 82C22, 82C31, 35Q91, 91B80, Probability |
| Description: | 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. 33 pages, 7 figures |
| Document Type: | Article |
| ISSN: | 1553-5231 1078-0947 |
| DOI: | 10.3934/dcds.2025126 |
| DOI: | 10.48550/arxiv.2406.05043 |
| Access URL: | http://arxiv.org/abs/2406.05043 |
| Rights: | arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....0b65ef3aef4ba037b889d89fab12cdd1 |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | 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 $μ> 0$), 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.<br />33 pages, 7 figures |
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| ISSN: | 15535231 10780947 |
| DOI: | 10.3934/dcds.2025126 |