Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.24383 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915700912685056 |
|---|---|
| author | Nguyen, Vinh Shvydkoy, Roman Tan, Changhui |
| author_facet | Nguyen, Vinh Shvydkoy, Roman Tan, Changhui |
| contents | We study the mean-field limit for a class of agent-based models describing flocking with nonlinear velocity alignment. Each agent interacts through a communication protocol $ϕ$ and a non-linear coupling of velocities given by the power law $A(\bv) = |\bv|^{p-2}\bv$, $p > 2$. The mean-field limit is proved in two settings -- deterministic and stochastic. We then provide quantitative estimates on propagation of chaos for deterministic case in the case of the classical fat-tailed kernels, showing an improved convergence rate of the $k$-particle marginals to a solution of the corresponding Vlasov equation. The stochastic version is addressed with multiplicative noise depending on the local interaction intensity, which leads to the associated Fokker-Planck-Alignment equation.
Our results extend the classical Cucker-Smale theory to the nonlinear framework which has received considerable attention in the literature recently. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24383 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mean-Field Limits of Deterministic and Stochastic Flocking Models with Nonlinear Velocity Alignment Nguyen, Vinh Shvydkoy, Roman Tan, Changhui Analysis of PDEs Probability 92D25, 35Q35 We study the mean-field limit for a class of agent-based models describing flocking with nonlinear velocity alignment. Each agent interacts through a communication protocol $ϕ$ and a non-linear coupling of velocities given by the power law $A(\bv) = |\bv|^{p-2}\bv$, $p > 2$. The mean-field limit is proved in two settings -- deterministic and stochastic. We then provide quantitative estimates on propagation of chaos for deterministic case in the case of the classical fat-tailed kernels, showing an improved convergence rate of the $k$-particle marginals to a solution of the corresponding Vlasov equation. The stochastic version is addressed with multiplicative noise depending on the local interaction intensity, which leads to the associated Fokker-Planck-Alignment equation. Our results extend the classical Cucker-Smale theory to the nonlinear framework which has received considerable attention in the literature recently. |
| title | Mean-Field Limits of Deterministic and Stochastic Flocking Models with Nonlinear Velocity Alignment |
| topic | Analysis of PDEs Probability 92D25, 35Q35 |
| url | https://arxiv.org/abs/2512.24383 |