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We investigate the level density for several ensembles of positive random matrices of a Wishart--like structure, $W=XX^{\dagger}$, where $X$ stands for a nonhermitian random matrix.
V. A. Marchenko and L. A. Pastur, The distribution of eigenvalues in certain sets of random matrices, Math. Sb
1967
Earlier work this paper cites.
F. G. Tricomi, Integral equations
1985
Earlier work this paper cites.
D. V. Voiculescu, K. J. Dykema and A. Nica, Free random variables
1992
Earlier work this paper cites.
A. Uhlmann, The metric of Bures and the geometric phase, in Groups and related Topics
1992
Earlier work this paper cites.
A. Nica and R. Speicher, R-diagonal pairs - a common approach to Haar unitarities and circular elements, Fields Institute Communications
1997
Earlier work this paper cites.
U. Haagerup and F. Larsen, Brown’s spectral distribution measure for R-diagonal elements in finite von Neumann algebras, Journal of Functional Analysis
2000
Earlier work this paper cites.
K. Życzkowski and H.-J. Sommers, Induced measures in the space of mixed quantum states, J. Phys
2001
Earlier work this paper cites.
B. Eynard, An introduction to Random Matrices
2001
Earlier work this paper cites.
K. A. Penson and A. I. Solomon, Coherent states from combinatorial sequences, pp. 527-530 in Quantum theory and symmetries
2002
Earlier work this paper cites.
S. T. Belinschi, The atoms of the free multiplicative convolution of two probability distributions, Integr. Eqn. Oper. Theory
2003
Earlier work this paper cites.
H.–J. Sommers and K. Życzkowski, Statistical properties of random density matrices, J. Phys
2004
Earlier work this paper cites.
T. Cabanal-Duvillard, A matrix representation of the Bercovici-Pata bijection, Electronic J. Probab
2005
Earlier work this paper cites.
P. J. Forrester, Log-gases and Random matrices
2010
Cited alongside, same era.
B. Collins, I. Nechita and K. Życzkowski, Random graph states, maximal flow and Fuss-Catalan distributions, J. Phys
2010
Cited alongside, same era.
W. Młotkowski, Fuss-Catalan numbers in noncommutative probability, Documenta Math
2010
Cited alongside, same era.
Z. Burda, A. Jarosz, G. Livan, M. A. Nowak and A. Świech, Eigenvalues and singular values of products of rectangular Gaussian random matrices, Phys. Rev
2010
Cited alongside, same era.
N. Alexeev, F. Götze and A. Tikhomirov, Asymptotic distribution of singular values of powers of random matrices, Lithuanian Math. J
2010
Cited alongside, same era.
K. Życzkowski, talk at 13-th Workshop on Harmonic Analysis, Bȩdlewo by Poznań, July 2010 (unpublished)
D.-Z. Liu, C. Song and Z.-D. Wang, On Explicit Probability Densities Associated with Fuss-Catalan Numbers, Proc. Am. Math. Soc
2011
Later among the works it cites.
Z. Burda, R. A. Janik and M. A. Nowak, Multiplication law and S-transform for non-hermitian random matrices, Phys. Rev
2011
Later among the works it cites.
J. Feinberg and A. Zee, Non-Gaussian non-hermitian random matrix theory: Phase transition and addition formalism, Nucl. Phys
2011
Later among the works it cites.
M. Hinz and W. Młotkowski, Free powers of the free Poisson measure, Colloquium Mathematicum
2011
Later among the works it cites.
Z. Burda, M.A. Nowak and A. Swiech, Spectral relations between products and powers of isotropic random matrices, Phys. Rev
2012
Later among the works it cites.
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2010
Cited alongside, same era.
V.A. Osipov, H.-J. Sommers, K. Życzkowski, Random Bures mixed states and the distribution of their purity, J. Phys
2010
Cited alongside, same era.
G. Akemann, J. Baik and P. Di Francesco (eds.), The Oxford Handbook of Random Matrix Theory
2011
Cited alongside, same era.
K. Życzkowski, K. A. Penson, I. Nechita and B. Collins, Generating random density matrices, J. Math. Phys. 52
2011
Cited alongside, same era.
A. Jarosz, Addition of free unitary random matrices II, Phys. Rev
2011
Cited alongside, same era.
T. Banica, S. Belinschi, M. Capitaine and B. Collins, Free Bessel laws, Canadian J. Math
2011
Cited alongside, same era.
K. A. Penson and K. Życzkowski, Product of Ginibre matrices: Fuss-Catalan and Raney distributions, Phys. Rev
2011
Cited alongside, same era.
G. Akemann, M. Kieburg and L. Wei, Singular value correlation functions for products of Wishart random matrices, J. Phys
2013
Later among the works it cites.
G. Akemann, J. R. Ipsen and M. Kieburg, Products of rectangular random matrices: Singular values and progressive scattering, Phys. Rev
2013
Later among the works it cites.
W. Młotkowski, K. A. Penson and K. Życzkowski, Densities of the Raney distributions, Documenta Math
2013
Later among the works it cites.
A. B. J. Kuijlaars and L. Zhang, Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits, Commun. Math. Phys
2014
Closest in time.
U. Haagerup and S. Möller, The law of large numbers for the free multiplicative convolution, Springer Proceedings in Mathematics and Statistics, Vol. 58, ed. T. M. Carlsen et al., (Springer, Berlin, 2014)
2014
Closest in time.
T. Neuschel, Plancherel-Rotach formulae for average characteristic polynomials of products of Ginibre random matrices and the Fuss-Catalan distribution, Random Matrices Theory Appl
2014
Closest in time.
P. J. Forrester and D.-Z. Liu, Raney distributions and random matrix theory, J. Stat. Phys
2015
Closest in time.