Propagation of chaos for maxima of 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: |
2022
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| _version_ | 1866917355593924608 |
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| author | Kolliopoulos, Nikolaos Larsson, Martin Zhang, Zeyu |
| author_facet | Kolliopoulos, Nikolaos Larsson, Martin Zhang, Zeyu |
| contents | We study the asymptotic behavior of the normalized maxima of real-valued diffusive particles with mean-field drift interaction. Our main result establishes propagation of chaos: in the large population limit, the normalized maxima behave as those arising in an i.i.d. system where each particle follows the associated McKean--Vlasov limiting dynamics. Because the maximum depends on all particles, our result does not follow from classical propagation of chaos, where convergence to an i.i.d. limit holds for any fixed number of particles but not all particles simultaneously. The proof uses a change of measure argument that depends on a delicate combinatorial analysis of the iterated stochastic integrals appearing in the chaos expansion of the Radon--Nikodym density. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_10018 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Propagation of chaos for maxima of particle systems with mean-field drift interaction Kolliopoulos, Nikolaos Larsson, Martin Zhang, Zeyu Probability 60K35, 60H10, 60F05, 60G70 We study the asymptotic behavior of the normalized maxima of real-valued diffusive particles with mean-field drift interaction. Our main result establishes propagation of chaos: in the large population limit, the normalized maxima behave as those arising in an i.i.d. system where each particle follows the associated McKean--Vlasov limiting dynamics. Because the maximum depends on all particles, our result does not follow from classical propagation of chaos, where convergence to an i.i.d. limit holds for any fixed number of particles but not all particles simultaneously. The proof uses a change of measure argument that depends on a delicate combinatorial analysis of the iterated stochastic integrals appearing in the chaos expansion of the Radon--Nikodym density. |
| title | Propagation of chaos for maxima of particle systems with mean-field drift interaction |
| topic | Probability 60K35, 60H10, 60F05, 60G70 |
| url | https://arxiv.org/abs/2206.10018 |