Large-population asymptotics for the maximum of diffusive particles with mean-field interaction in the noises
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929210730217472 |
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| author | Kolliopoulos, Nikolaos Sanchez, David Xiao, Amy |
| author_facet | Kolliopoulos, Nikolaos Sanchez, David Xiao, Amy |
| contents | We study the $N \to \infty$ limit of the normalized largest component in some systems of $N$ diffusive particles with mean-field interaction. By applying a universal time change, the interaction in noises is transferred to the drift terms, and the asymptotic behavior of the maximum becomes well-understood due to existing results in the literature. We expect that the normalized maximum in the original setting has the same limiting distribution as that of i.i.d copies of a solution to the corresponding McKean-Vlasov SDE and we present some results and numerical simulations that support this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08344 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large-population asymptotics for the maximum of diffusive particles with mean-field interaction in the noises Kolliopoulos, Nikolaos Sanchez, David Xiao, Amy Probability 60K35, 60H10, 60F05, 60G70 We study the $N \to \infty$ limit of the normalized largest component in some systems of $N$ diffusive particles with mean-field interaction. By applying a universal time change, the interaction in noises is transferred to the drift terms, and the asymptotic behavior of the maximum becomes well-understood due to existing results in the literature. We expect that the normalized maximum in the original setting has the same limiting distribution as that of i.i.d copies of a solution to the corresponding McKean-Vlasov SDE and we present some results and numerical simulations that support this conjecture. |
| title | Large-population asymptotics for the maximum of diffusive particles with mean-field interaction in the noises |
| topic | Probability 60K35, 60H10, 60F05, 60G70 |
| url | https://arxiv.org/abs/2401.08344 |