论文标题
与平均场漂移相互作用的粒子系统最大值的混乱传播
Propagation of chaos for maxima of particle systems with mean-field drift interaction
论文作者
论文摘要
我们研究了具有平均场漂移相互作用的实值扩散颗粒的标准化最大值的渐近行为。我们的主要结果建立了混乱的传播：在较大的人口限制中，标准化的最大值是在I.I.D.每个粒子都遵循相关的McKean-Vlasov限制动力学的系统。由于最大值取决于所有粒子，因此我们的结果并不依赖于混乱的经典传播，其中收敛到I.I.D.极限对于任何固定数量的粒子都持有，但并非所有粒子同时保持。该证明使用了量度参数的更改，取决于迭代的随机积分的精致组合分析，出现在ra的混乱膨胀中 - nikodym密度。
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.
