论文标题
扭曲的COE矩阵矩的收敛
Convergence of moments of twisted COE matrices
论文作者
论文摘要
我们研究了由置换矩阵扰动的圆形正交集合的矩阵的特征值矩。更确切地说，我们调查了提高到$ k $的特征值的总和的差异，用于$ k $，但修复了$ k $，并且在较大的矩阵大小的限制中。我们发现，当定义扰动合奏的置换仅具有较长的周期时，答案是通用的，并且以特别快的速度接近圆形单一合奏的相应瞬间：订单的错误是$ 1/n^3 $，订单条款$ 1/n $和$ 1/n $和$ 1/n^2 $由于取消而消失了。我们使用Weingarten演算证明了这种收敛速率，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。
We investigate eigenvalue moments of matrices from Circular Orthogonal Ensemble multiplicatively perturbed by a permutation matrix. More precisely we investigate variance of the sum of the eigenvalues raised to power $k$, for arbitrary but fixed $k$ and in the limit of 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 $1/N^3$ and the terms of orders $1/N$ and $1/N^2$ 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.
