𝑉-law for random block matrices under the generalized Lindeberg condition
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Vyacheslav L. Girko
Abstract
The V-law under generalized Lindeberg condition for the independent blocks of random matrices having double stochastic matrix of covariances and different expectations of their array is proven.
References
[1] V. L. Girko, V- transform (in Russian), Dokl. AN USSR. Ser. A 5-6 (1982), no. 3. Search in Google Scholar
[2] 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
[3] V. L. Girko, The V-density of eigenvalues of nonsymmetric random matrices and rigorous proof of the strong circular law, Random Oper. Stoch. Equ. 5 (1997), no. 4, 371–406. 10.1515/rose.1997.5.4.371Search 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, Random block matrix density and SS-law, Random Oper. Stoch. Equ. 8 (2000), no. 2, 189–194. 10.1515/rose.2000.8.2.189Search in Google Scholar
[6] V. L. Girko, Theory of Stochastic Canonical Equations. Vol. I and II, Math. Appl. 535, Kluwer Academic, Dordrecht, 2001. 10.1007/978-94-010-0989-8Search in Google Scholar
[7] V. L. Girko, The circular law. Twenty years later. III, Random Oper. Stoch. Equ. 13 (2005), no. 1, 53–109. 10.1515/1569397053300946Search in Google Scholar
[8] V. L. Girko, 35 years of the Inverse Tangent Law, Random Oper. Stoch. Equ. 19 (2011), no. 4, 299–312. 10.1515/ROSE.2011.017Search in Google Scholar
[9] V. L. Girko, The circular law. Thirty year later, Random Oper. Stoch. Equ. 20 (2012), no. 2, 143–187. 10.1515/rose-2012-0007Search in Google Scholar
[10]
V. L. Girko,
30 years of general statistical analysis and canonical equation
[11] V. L. Girko, From the first rigorous proof of the circular law in 1984 to the circular law for block random matrices under the generalized Lindeberg condition, Random Oper. Stoch. Equ. 26 (2018), no. 2, 89–116. 10.1515/rose-2018-0008Search in Google Scholar
[12]
V. L. Girko,
Girko’s circular law: Let λ be eIgenvalues of a set of random
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Articles in the same Issue
- Frontmatter
- Hyers–Ulam stability for coupled random fixed point theorems and applications to periodic boundary value random problems
- Internal stabilization of stochastic 3D Navier–Stokes–Voigt equations with linearly multiplicative Gaussian noise
- V-density for eigenvalues of random block matrices with independent blocks whose entries have different variances and expectations
- The RESPECT method. Simple proof of finding estimates from below for minimal singular eigenvalues of random matrices whose entries have zero means and bounded variances
- 𝑉-law for random block matrices under the generalized Lindeberg condition
- Continuous distributions whose functions preserve tails of an 𝐴-continued fraction representation of numbers
Articles in the same Issue
- Frontmatter
- Hyers–Ulam stability for coupled random fixed point theorems and applications to periodic boundary value random problems
- Internal stabilization of stochastic 3D Navier–Stokes–Voigt equations with linearly multiplicative Gaussian noise
- V-density for eigenvalues of random block matrices with independent blocks whose entries have different variances and expectations
- The RESPECT method. Simple proof of finding estimates from below for minimal singular eigenvalues of random matrices whose entries have zero means and bounded variances
- 𝑉-law for random block matrices under the generalized Lindeberg condition
- Continuous distributions whose functions preserve tails of an 𝐴-continued fraction representation of numbers
