Abstract
The Circular Law under Lindeberg’s condition for the independent blocks of random matrices having zero expectations and double stochastic matrix of covariances of their array is proven.
Dedicated to the twenty-fifth anniversary of the Journal Random Operators and Stochastic Equations
References
[1] J. Aljadeff, D. Renfrew and M. Stern, Eigenvalues of block structured asymmetric random matrices, J. Math. Phys. 56 (2015), no. 10, Article ID 103502. 10.1063/1.4931476Search in Google Scholar
[2] J. Alt, L. Erdős, T. Krüger and Y. Nemish, Location of the spectrum of Kronecker random matrices, preprint (2018), https://arxiv.org/abs/1706.08343v3. 10.1214/18-AIHP894Search in Google Scholar
[3] V. L. Girko, Theory of Random Determinants, Math. Appl. (Soviet Series) 45, Kluwer Academic, Dordrecht, 1990. 10.1007/978-94-009-1858-0Search in Google Scholar
[4] V. L. Girko, An Introduction to Statistical Analysis of Random Arrays, VSP, Utrecht, 1998. 10.1515/9783110916683Search in Google Scholar
[5] V. L. Girko, Theory of Stochastic Canonical Equations. Vol. I and II, Math. Appl., Kluwer Academic, Dordrecht, 2001. 10.1007/978-94-010-0989-8Search in Google Scholar
[6] V. L. Girko, The Circular Law. Thirty years later, Random Oper. Stoch. Equ. 20 (2012), no. 2, 143–187. 10.1515/rose-2012-0007Search in Google Scholar
[7]
V. L. Girko,
The circle law. Girko’s circular law: Let λ be eigenvalues of a set of random
[8] F. Juhsz, On the structural eigenvalues of block random matrices, Linear Algebra Appl. 246 (1996), 225–231. 10.1016/0024-3795(94)00356-4Search in Google Scholar
[9] V. A. Marchenko and L. A. Pastur, Distribution of the eigenvalues in certain sets of random matrices (in Russian), Mat. Sb. 1 (1967), 457–483. 10.1070/SM1967v001n04ABEH001994Search in Google Scholar
[10] H. Nguyen and S. O’Rourke, On the concentration of random multilinear forms and the universality of random block matrices, Probab. Theory Related Fields 162 (2015), no. 1–2, 97–154. 10.1007/s00440-014-0567-7Search in Google Scholar
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