Accessible Requires Authentication Published by De Gruyter December 1, 2011

35 years of the Inverse Tangent Law

Vyacheslav Girko
From the journal

Abstract

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.

Received: 2008-10-16
Accepted: 2009-03-07
Published Online: 2011-December
Published in Print: 2011-December

de Gruyter 2011