Asymptotic properties of large random matrices with independent entries
Asymptotic properties of large random matrices with independent entries
复制标题
DOI：
10.1063/1.531589
复制
发表时间：
1996-10-01
影响因子：
1.3
通讯作者：
Pastur, LA
中科院分区：
文献类型：
--
作者：
Khorunzhy, AM;Khoruzhenko, BA;Pastur, LA
我们研究 n x n 实数对称矩阵 H = [(1 + delta(jk)) W-jk root n](n)(j,k=1) 的求解的归一化迹 g(n)(z) = n(-1) tr(H - zI)(-1) ，假设它们的条目是独立的，但不一定是同分布的随机变量。我们开发了一种严格的方法，对大于或等于 eta(0) 的 g(n)(z) 矩进行渐近分析，其中 eta(0) 由 W-jk 的二阶矩确定。通过使用这种方法，我们找到期望 E(g(n)(z)) 和连接相关器 E{g(n)(z(1))g(n)(z(2))} - E{g(n)(z(1))}E{g(n)(z(2))} 的渐近形式。我们还证明集中迹 ng(n)(z) - E{ng(n)(z)} 在极限 n = 无穷大时具有高斯分布。基于这些结果，我们提出了启发式论证，支持此类随机矩阵系综的局部特征值统计的普遍性。 (C) 1996 年美国物理研究所。
We study the normalized trace g(n)(z) = n(-1) tr(H - zI)(-1) of the resolvent of n x n real symmetric matrices H = [(1 + delta(jk)) W-jk root n](n)(j,k=1) assuming that their entries are independent but not necessarily identically distributed random variables. We develop a rigorous method of asymptotic analysis of moments of g(n)(z) for \Jz\ greater than or equal to eta(0) where eta(0) is determined by the second moment of W-jk. By using this method we find the asymptotic form of the expectation E(g(n)(z)) and of the connected correlator E{g(n)(z(1))g(n)(z(2))} - E{g(n)(z(1))}E{g(n)(z(2))}. We also prove that the centralized trace ng(n)(z) - E{ng(n)(z)} has the Gaussian distribution in the limit n = infinity. Based on these results we present heuristic arguments supporting the universality property of the local eigenvalue statistics for this class of random matrix ensembles. (C) 1996 American Institute of Physics.