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

Nikolaos Kolliopoulos, David Sanchez and Amy Xiao

Statistics & Probability Letters, 2024, vol. 212, issue C

Abstract: We study the N→∞ 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.

Keywords: Mean-field systems; Propagation of chaos; Extreme value distributions; Weak convergence; Numerical simulations (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110150

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