Moment-Constrained Vector Reconstruction of Random-Matrix Statistics in Finite Hilbert Spaces (opens in new tab)

Random-matrix statistics are usually imposed at the level of matrix entries or spectral correlations. Here we formulate a complementary inverse problem: can a matrix with prescribed random-matrix moments be generated from a structured set of latent vectors? We introduce a pair-resolved vector ansatz consisting of two vector families, P and Q, construct a complex-symmetric non-Hermitian matrix M = a1P P T + a2QQT . The transpose is intentiona...