发表机构
École Normale Supérieure de Rennes（雷恩高等师范学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究带稳定公共噪声的均值场粒子系统，通过泊松构造和分位数耦合，证明了条件波动的高斯极限，并揭示了内生秩响应对临界行为的影响。
AI 中文摘要
我们研究了环面上光滑均值场粒子系统的条件波动，该系统具有内生对称稳定公共跳跃，指数为$0<\alpha<1$。在公共泊松构造下，正带估计使经验接受误差在采样尺度上可忽略，并在负Sobolev空间中产生泛函中心极限定理。给定完整泊松主过程的条件法则在概率上收敛于中心高斯核。在一维情形中，分位数耦合将该极限转移到微观标记上，其相对尾部余项为$O(x^{-\rho})$，其中$\rho>\alpha/2$。在量化的二阶尾部展开下，我们识别了内生秩响应：它在临界点处移动条件高斯均值，并且当响应非零时在临界点以下主导采样。我们还建立了秩误差的独立稳定到布朗过渡。最后，一个在秩耦合和时钟耦合下具有相同微观法则的平移模型在前一种耦合中允许泛函高斯极限，但在后一种耦合中在极限中心没有发散的加性路径归一化。
英文摘要
We study conditional fluctuations of smooth mean-field particle systems on a torus with endogenous symmetric stable common jumps of index $0<α<1$. Under a common Poisson construction, a positive-strip estimate makes empirical acceptance errors negligible at the sampling scale and yields a functional central limit theorem in a negative Sobolev space. The conditional laws, given the full Poisson master, converge in probability to a centered Gaussian kernel. In dimension one, quantile coupling transfers this limit to microscopic marks whose relative tail remainder is $O(x^{-ρ})$ with $ρ>α/2$. Under a quantified second-order tail expansion, we identify the endogenous rank response: it shifts the conditional Gaussian mean at criticality and dominates sampling below criticality whenever the response is nonzero. We also establish a separate stable-to-Brownian transition for the rank error. Finally, a translation model with identical microscopic laws under rank and clock couplings admits a functional Gaussian limit in the former coupling but no diverging additive path normalization at the limiting center in the latter.
Comments32 pages, 1 table
