We investigate eigenvalue moments of matrices from the circular orthogonal ensemble multiplicatively perturbed by a permutation matrix. More precisely, we investigate the variance of the sum of the eigenvalues raised to power k for arbitrary but fixed k and in the limit of a large matrix size. We find that when the permutation defining the perturbed ensemble has only long cycles, the answer is universal and approaches the corresponding moment of the circular unitary ensemble with a particularly fast rate: the error is of order 1/N³ and the terms of orders 1/N and 1/N² disappear due to cancellations. We prove this rate of convergence using Weingarten calculus and classifying the contributing Weingarten functions first in terms of a graph model and then algebraically.

中文翻译：

---

扭曲 COE 矩阵矩的收敛

我们从被置换​​矩阵乘法扰动的圆形正交系综中研究矩阵的特征值矩。更确切地说，我们提出调查权力的特征值的总和的方差ķ任意但固定ķ和大矩阵大小的限制。我们发现，当定义扰动系综的置换只有长周期时，答案是通用的，并且以特别快的速度接近圆形酉系综的对应矩：误差为 1/ N ³阶，而阶数为 1 / N和 1/ N ²因取消而消失。我们使用 Weingarten 微积分证明了这种收敛速度，并首先根据图模型然后通过代数对贡献的 Weingarten 函数进行分类。