Physics – Mathematical Physics
Scientific paper
2012-02-24
Physics
Mathematical Physics
17 pages, 24 figures, 102 equations
Scientific paper
Inspired by the theory of quantum information, I use two non-Hermitian random matrix models - a weighted sum of circular unitary ensembles and a product of rectangular Ginibre unitary ensembles - as building blocks of three new products of random matrices which are generalizations of the Bures model. I apply the tools of both Hermitian and non-Hermitian free probability to calculate the mean densities of their eigenvalues and singular values in the thermodynamic limit, along with their divergences at zero; the results are supported by Monte Carlo simulations. I pose and test conjectures concerning the relationship between the two densities (exploiting the notion of the N-transform), the shape of the mean domain of the eigenvalues (an extension of the single ring theorem), and the universal behavior of the mean spectral density close to the domain's borderline (using the complementary error function).
Jarosz Andrzej
No associations
LandOfFree
Generalized Bures products from free probability does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Generalized Bures products from free probability, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Bures products from free probability will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-78209