On the asymptotic distribution of block-modified random matrices
- Department of Probability and Statistics, CIMAT, Guanajuato (Mexico)
- Zentrum Mathematik, M5, Technische Universität München, Boltzmannstrasse 3, 85748 Garching, Germany and CNRS, Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, UPS, F-31062 Toulouse (France)
- Department of Mathematical Structure Theory, Technische Universität Graz, Steyrergasse 30/III, 8010 Graz (Austria)
We study random matrices acting on tensor product spaces which have been transformed by a linear block operation. Using operator-valued free probability theory, under some mild assumptions on the linear map acting on the blocks, we compute the asymptotic eigenvalue distribution of the modified matrices in terms of the initial asymptotic distribution. Moreover, using recent results on operator-valued subordination, we present an algorithm that computes, numerically but in full generality, the limiting eigenvalue distribution of the modified matrices. Our analytical results cover many cases of interest in quantum information theory: we unify some known results and we obtain new distributions and various generalizations.
- OSTI ID:
- 22479620
- Journal Information:
- Journal of Mathematical Physics, Vol. 57, Issue 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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