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

Author

Listed:
  • Kolliopoulos, Nikolaos
  • Sanchez, David
  • Xiao, Amy

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.

Suggested Citation

  • Kolliopoulos, Nikolaos & Sanchez, David & Xiao, Amy, 2024. "Large-population asymptotics for the maximum of diffusive particles with mean-field interaction in the noises," Statistics & Probability Letters, Elsevier, vol. 212(C).
    • Handle: RePEc:eee:stapro:v:212:y:2024:i:c:s0167715224001196
    DOI: 10.1016/j.spl.2024.110150
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