Essentials of the kinetic theory of multi-agent systems
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916652798443520 |
|---|---|
| author | Loy, Nadia Tosin, Andrea |
| author_facet | Loy, Nadia Tosin, Andrea |
| contents | In this paper, we present a critical collection of essential mathematical tools and techniques for the analysis of Boltzmann-type kinetic equations, which in recent years have established themselves as a flexible and powerful paradigm to model interacting multi-agent systems. We consider, in particular, scalar equations implementing linear symmetric interaction rules, for which we develop the theory of well-posedness, trend to equilibrium, and Fokker-Planck asymptotics by relying extensively on Fourier methods. We also outline the basics of Monte Carlo algorithms for the numerical solution of such equations. Finally, we elaborate the theory further for Boltzmann-type equations on graphs, a recent generalisation of the standard setting motivated by the modelling of networked multi-agent systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11554 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Essentials of the kinetic theory of multi-agent systems Loy, Nadia Tosin, Andrea Mathematical Physics 35Q20, 35Q70, 82C40 In this paper, we present a critical collection of essential mathematical tools and techniques for the analysis of Boltzmann-type kinetic equations, which in recent years have established themselves as a flexible and powerful paradigm to model interacting multi-agent systems. We consider, in particular, scalar equations implementing linear symmetric interaction rules, for which we develop the theory of well-posedness, trend to equilibrium, and Fokker-Planck asymptotics by relying extensively on Fourier methods. We also outline the basics of Monte Carlo algorithms for the numerical solution of such equations. Finally, we elaborate the theory further for Boltzmann-type equations on graphs, a recent generalisation of the standard setting motivated by the modelling of networked multi-agent systems. |
| title | Essentials of the kinetic theory of multi-agent systems |
| topic | Mathematical Physics 35Q20, 35Q70, 82C40 |
| url | https://arxiv.org/abs/2503.11554 |