Propagation of chaos for point processes induced by particle systems with mean-field drift interaction
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914412375310336 |
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| author | Kolliopoulos, Nikolaos Larsson, Martin Zhang, Zeyu |
| author_facet | Kolliopoulos, Nikolaos Larsson, Martin Zhang, Zeyu |
| contents | We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: it has the same weak limit as the point process induced by i.i.d. copies of the solution of a limiting Mckean--Vlasov equation. This weak limit is a Poisson point process whose intensity measure is related to classical extreme value distributions. In particular, this yields the limiting distribution of the normalized upper order statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11426 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Propagation of chaos for point processes induced by particle systems with mean-field drift interaction Kolliopoulos, Nikolaos Larsson, Martin Zhang, Zeyu Probability 60K35, 60H10, 60F05, 60G70 We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: it has the same weak limit as the point process induced by i.i.d. copies of the solution of a limiting Mckean--Vlasov equation. This weak limit is a Poisson point process whose intensity measure is related to classical extreme value distributions. In particular, this yields the limiting distribution of the normalized upper order statistics. |
| title | Propagation of chaos for point processes induced by particle systems with mean-field drift interaction |
| topic | Probability 60K35, 60H10, 60F05, 60G70 |
| url | https://arxiv.org/abs/2303.11426 |