  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.
