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

Pub Date : 2024-05-10 DOI:10.1016/j.spl.2024.110150
Nikolaos Kolliopoulos , David Sanchez , Amy Xiao
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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.

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在噪声中具有均场相互作用的扩散粒子最大值的大群体渐近论
我们研究了具有均场相互作用的N个扩散粒子系统中归一化最大分量的N→∞极限。通过应用普遍的时间变化,噪声中的相互作用被转移到漂移项中,由于文献中已有的结果,最大值的渐近行为变得很好理解。我们预计原始设置中的归一化最大值与相应麦金-弗拉索夫 SDE 解的 i.i.d 副本具有相同的极限分布,并给出了支持这一猜想的一些结果和数值模拟。
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