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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre

CiteScore 2018: 0.26

SCImago Journal Rank (SJR) 2018: 0.142
Source Normalized Impact per Paper (SNIP) 2018: 0.375

Mathematical Citation Quotient (MCQ) 2018: 0.11

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Volume 19, Issue 4


35 years of the Inverse Tangent Law

Vyacheslav Girko


The distribution functions of the solutions of the systems of linear algebraic equations (SLAE) , in general, have a cumbersome form; the order of these systems in some practical problems is large, therefore, the asymptotic behavior of the solutions should be studied in increasing order n of the system to infinity. A general form of the limit theorems of solutions of the systems of linear algebraic equations

with independent random coefficients and components , i, j 1, . . . , n, are given in this survey. By the tradition of choosing the names of laws in probability theory (Arcsine law, Law of iterated logarithm, etc.) we call the unusual behavior of the solutions of (SLAERC) as Inverse Tangent Law.

About the article

Received: 2008-10-16

Accepted: 2009-03-07

Published in Print: 2011-12-01

Citation Information: Random Operators and Stochastic Equations, Volume 19, Issue 4, Pages 299–312, ISSN (Online) 1569-397x, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/ROSE.2011.017.

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