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

Understand

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.