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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 2, Pages 266–280 (Mi tvp2527)

A representation of random matrices in orispherical coordinates and its application to telegraph equations

V. N. Tutubalin

Moscow

Abstract: A central limit theorem for products $g(n)=g_1g_2…g_n$ of random matrices $g_1,g_2,…,g_n$ was considered in an earlier paper [5], a representation
$$g(n)=x(n)d(n)u(n)$$
with orthogonal (unitary) matrices $x(n)$ and $u(n)$ and diagonal $d(n)$ being investigated. Products of random matrices, as far as we know, arise in the theory of telegraph equations [9], [10], where the matrices $g_1,…,g_n$ are symplectic, but unitary matrices have no immediate physical interpretation in the frame of this theory. From the viewpoint of possible applications a more physical form of central limit theorem is highly desirable. Such forms are given in the present paper.

Full text: PDF file (898 kB)

English version:
Theory of Probability and its Applications, 1973, 17:2, 255–268

Bibliographic databases:

Citation: V. N. Tutubalin, “A representation of random matrices in orispherical coordinates and its application to telegraph equations”, Teor. Veroyatnost. i Primenen., 17:2 (1972), 266–280; Theory Probab. Appl., 17:2 (1973), 255–268

Citation in format AMSBIB
\Bibitem{Tut72} \by V.~N.~Tutubalin \paper A~representation of random matrices in orispherical coordinates and its application to telegraph equations \jour Teor. Veroyatnost. i Primenen. \yr 1972 \vol 17 \issue 2 \pages 266--280 \mathnet{http://mi.mathnet.ru/tvp2527} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=307305} \zmath{https://zbmath.org/?q=an:0267.60028} \transl \jour Theory Probab. Appl. \yr 1973 \vol 17 \issue 2 \pages 255--268 \crossref{https://doi.org/10.1137/1117030} 

• http://mi.mathnet.ru/eng/tvp2527
• http://mi.mathnet.ru/eng/tvp/v17/i2/p266

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This publication is cited in the following articles:
1. A. V. Letchikov, “Products of unimodular independent random matrices”, Russian Math. Surveys, 51:1 (1996), 49–96