Imagine you are looking for the eigenvalue distribution
B:= UU* (1/n)
of a product, where U describes the upper left lxk block of the matrix V, which diagonalises the adjacency matrix of a d-regular graph. U* means the complex conjugate matrix of U. How do I apply techniques such as the method of moments or Steltje’s transformation to obtain an explicit prescription of the limit distribution for the matrix B for example if d = 2?
Need some explicit information/literature or help to derive the limit distribution of the matrix B (product of matrices with structure in the eigenvectors contrary to the usual Wishart ensemble) for large l, k.