The \(G\)-pencil law under \(G\)-Lindeberg condition. The canonical equation \(K_{98}\) and \(G\)-logarithmic law

DOI10.1515/rose-2022-2072zbMath1486.15038OpenAlexW4220963383MaRDI QIDQ2121582

Borys V. Shevchuk, Larissa D. Shevchuk, Vyacheslav L. Girko

Publication date: 4 April 2022

Published in: Random Operators and Stochastic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/rose-2022-2072

zbMATH Keywords

random matricescanonical equation

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Random matrices (algebraic aspects) (15B52)

Cites Work

• 30 years of general statistical analysis and canonical equation \(K_{60}\) for Hermitian matrices \((A+BUC)(A+BUC)^*\), where \(U\) is a random unitary matrix
• From the first rigorous proof of the circular law in 1984 to the circular law for block random matrices under the generalized Lindeberg condition
• VICTORIA transform, RESPECT and REFORM methods for the proof of the \(G\)-permanent pencil law under \(G\)-Lindeberg condition for some random matrices from \(G\)-elliptic ensemble
• The V-density of eigenvalues of non symmetric random matrices and rigorous proof of the strong Circular law
• Random block matrix density and SS-Law
• The Circular Law. Thirty years later
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