The Pearcey process is a universal point process in random matrix theory and depends on a parameter ρ ∈ ℝ. Let N(x) be the random variable that counts the number of points in this process that fall in the interval [−x,x]. In this note, we establish the following global rigidity upper bound: lims→∞ℙ supx>s N(x) −33 4π x4 3 −3ρ 2πx2 3 log x ≤ 42 3π + 𝜖 = 1, where 𝜖 > 0 is arbitrary. We also obtain a similar upper bound for the maximum deviation of the points, and a central limit theorem for the individual fluctuations. The proof is short and combines a recent result of Dai, Xu and Zhang with another result of Charlier and Claeys.

中文翻译：

---

Pearcey 过程的最大偏差的上限

Pearcey 过程是随机矩阵理论中的一个通用点过程，它依赖于一个参数ρ ∈ ℝ. 让ñ(X)是计算此过程中落在区间内的点数的随机变量[-X,X]. 在本说明中，我们建立了以下全局刚性上限： 林s→∞ℙ 支持X>s ñ(X) -33 4π X4 3 -3ρ 2πX2 3 日志 X ≤ 42 3π + 𝜖 = 1, 在哪里𝜖 > 0是任意的。我们还获得了点的最大偏差的类似上限，以及单个波动的中心极限定理。证明很简短，将 Dai、Xu 和 Zhang 的最新结果与 Charlier 和 Claeys 的另一个结果相结合。