Large-population asymptotics for the maximum of diffusive particles with mean-field interaction in the noises

Nikolaos Kolliopoulos; David Sanchez; Amy Xiao

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arXiv · 2401.08344

Large-population asymptotics for the maximum of diffusive particles with mean-field interaction in the noises

Nikolaos Kolliopoulos·David Sanchez·Amy Xiao

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Abstract

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.

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BibTeX RIS

Nikolaos Kolliopoulos, David Sanchez, Amy Xiao. 2024-01-16. Large-population asymptotics for the maximum of diffusive particles with mean-field interaction in the noises. https://arxiv.org/abs/2401.08344

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