Determinantal correlations for classical projection processes

Recent applications in queuing theory and statistical mechanics have isolated the process formed by the eigenvalues of successive sub-matrices of the GUE. Analogous eigenvalue processes, formed in general from the eigenvalues of nested sequences of matrices resulting from random corank-1 projections of classical random matrix ensembles, are identified for the LUE and JUE. The correlations for all these processes can be computed in a unified way. The resulting expressions can then be analyzed in various scaling limits. At the soft edge, with the rank of the sub-matrices differing by an amount proportional to N2/3, the scaled correlations coincide with those known from the soft edge scaling of the Dyson Brownian motion model