Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance (correlation) matrix. Results can be applied in various problems...

We consider a covariance matrix composed of asymmetric and free random Lévy matrices. We use the results of free random variables to derive an algebraic equation for the resolvent and solve it to extract the spectral density. For an appropriate choice of asymmetry and Lévy index α/2=34 the...

Coordination among many interdependent actors in complex product development projects is recognized as a key activity in organizational theory. It is well known that this coordination becomes progressively more difficult with project size, but we do not yet sufficiently understand whether this...

We investigate the origin of order in the low-lying spectra of many-body systems with random two-body interactions. Our study based both on analytical as well as on numerical arguments shows that except for the most J-stretched states, the ground states in the higher J-sectors are more orderly...