A criterion for proving entropy chaos on path space
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914477224493056 |
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| author | Borasi, Luigi De Vecchi, Francesco Carlo Ugolini, Stefania |
| author_facet | Borasi, Luigi De Vecchi, Francesco Carlo Ugolini, Stefania |
| contents | A criterion for proving a strong form of propagation of chaos on the path space, known as entropy chaos, for a general interacting diffusion system is proposed. Our analysis focuses on the class of conservative diffusions introduced by Carlen, which are characterized by infinitesimal characteristic pairs, that is, a time-marginal probability density and a current velocity field. A key property of this broad class is that the processes remain diffusions under time-reversal. We prove that, given a suitable bound on the relative entropy (with respect to the Wiener measure) and the weak convergence of both drifts and fixed-time marginal densities, strong entropy chaos at the process level is achieved in the infinite particle limit, provided the limit drift satisfies a specific regularity condition. This stochastic framework encompasses various singular interacting particle systems and their related asymptotic scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14427 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A criterion for proving entropy chaos on path space Borasi, Luigi De Vecchi, Francesco Carlo Ugolini, Stefania Probability 60J60, 60K35, 81S20, 94A17 A criterion for proving a strong form of propagation of chaos on the path space, known as entropy chaos, for a general interacting diffusion system is proposed. Our analysis focuses on the class of conservative diffusions introduced by Carlen, which are characterized by infinitesimal characteristic pairs, that is, a time-marginal probability density and a current velocity field. A key property of this broad class is that the processes remain diffusions under time-reversal. We prove that, given a suitable bound on the relative entropy (with respect to the Wiener measure) and the weak convergence of both drifts and fixed-time marginal densities, strong entropy chaos at the process level is achieved in the infinite particle limit, provided the limit drift satisfies a specific regularity condition. This stochastic framework encompasses various singular interacting particle systems and their related asymptotic scenarios. |
| title | A criterion for proving entropy chaos on path space |
| topic | Probability 60J60, 60K35, 81S20, 94A17 |
| url | https://arxiv.org/abs/2604.14427 |