Quantitative relative entropy estimates on the whole space for convolution interaction forces
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910299565588480 |
|---|---|
| author | Nikolaev, Paul Prömel, David J. |
| author_facet | Nikolaev, Paul Prömel, David J. |
| contents | Quantitative estimates are derived, on the whole space, for the relative entropy between the joint law of random interacting particles and the tensorized law at the limiting systeme. The developed method combines the relative entropy method under the moderated interaction scaling introduced by Oeschläger, and the propagation of chaos in probability. The result includes the case that the interaction force does not need to be a potential field. Furthermore, if the interaction force is a potential field, with a convolutional structure, then the developed estimate also provides the modulated energy estimates. Moreover, we demonstrate propagation of chaos for large stochastic systems of interacting particles and discuss possible applications to various interacting particle systems, including the Coulomb interaction case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08938 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative relative entropy estimates on the whole space for convolution interaction forces Nikolaev, Paul Prömel, David J. Probability Analysis of PDEs 35D30, 35Q70, 60K35 Quantitative estimates are derived, on the whole space, for the relative entropy between the joint law of random interacting particles and the tensorized law at the limiting systeme. The developed method combines the relative entropy method under the moderated interaction scaling introduced by Oeschläger, and the propagation of chaos in probability. The result includes the case that the interaction force does not need to be a potential field. Furthermore, if the interaction force is a potential field, with a convolutional structure, then the developed estimate also provides the modulated energy estimates. Moreover, we demonstrate propagation of chaos for large stochastic systems of interacting particles and discuss possible applications to various interacting particle systems, including the Coulomb interaction case. |
| title | Quantitative relative entropy estimates on the whole space for convolution interaction forces |
| topic | Probability Analysis of PDEs 35D30, 35Q70, 60K35 |
| url | https://arxiv.org/abs/2401.08938 |