标题： Wishart矩阵的渐近特征值分布，其成分不是独立同分布的 显示英文标题

标题： Asymptotic Eigenvalue Distribution of Wishart Matrices whose Components are not Independently and Identically Distributed

摘要： 在本工作中，通过复制分析和信念传播方法分析了由其成分既不独立也不同分布的随机矩阵地特征值分布。 特别是，我们考虑了成分独立但不同分布的情况；例如，每行或每列中的成分可能为{独立同分布}。 我们还考虑了成分之间相互关联的更一般情况。 我们在仅做出弱假设的情况下使用复制方法，以确定渐近特征值分布并基于信念传播推导出一种算法。 我们的一个发现支持了从费曼图获得的结果。 我们展示了几个数值实验的结果，以验证我们提出的方法。 显示英文摘要

摘要： In the present work, eigenvalue distributions defined by a random rectangular matrix whose components are neither independently nor identically distributed are analyzed using replica analysis and belief propagation. In particular, we consider the case in which the components are independently but not identically distributed; for example, only the components in each row or in each column may be {identically distributed}. We also consider the more general case in which the components are correlated with one another. We use the replica approach while making only weak assumptions in order to determine the asymptotic eigenvalue distribution and to derive an algorithm for doing so, based on belief propagation. One of our findings supports the results obtained from Feynman diagrams. We present the results of several numerical experiments that validate our proposed methods.