随机GOE矩阵特征多项式的负矩与奇异性主导的强涨落
Negative moments of characteristic polynomials of random GOE matrices and singularity-dominated strong fluctuations
摘要：
本文计算了高斯正交包络（GOE）中N × N随机矩阵的（正则化）特征多项式在极限下的负整数矩为$N \to \infty$ .这些结果与Berry & Keating最近的一个猜想非常一致，该猜想是由奇异性主导的强涨落理论中开发的技术所激发的。这是第一个例子中，使用这些技术得到的非平凡的预测已被证明。
英文摘要：
We calculate the negative integer moments of the (regularized) characteristic polynomials of N x N random matrices taken from the Gaussian Orthogonal Ensemble (GOE) in the limit as $N \to \infty$. The results agree nontrivially with a recent conjecture of Berry & Keating motivated by techniques developed in the theory of singularity-dominated strong fluctuations. This is the first example where nontrivial predictions obtained using these techniques have been proved.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
