Abstract:
A central limit theorem for products g(n)=g1g2…gn of random matrices g1,g2,…,gn 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 g1,…,gn 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.
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
\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://mathscinet.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}
Linking options:
https://www.mathnet.ru/eng/tvp2527
https://www.mathnet.ru/eng/tvp/v17/i2/p266
This publication is cited in the following 6 articles:
A. V. Letchikov, “Products of unimodular independent random matrices”, Russian Math. Surveys, 51:1 (1996), 49–96
V. L. Girko, “Limit theorems for products of independent random matrices with positive elements”, Theory Probab. Appl., 27:4 (1983), 837–844
“Summary of Papers Presented at Sessions of the Probability and Statistics Seminar in the Mathematical Institute of the USSR Academy of Sciences, 1977”, Theory Probab. Appl., 23:2 (1979), 439–457
S. V. Rezničenko, “An investigation of systems of coupled-mode equations with small random disturbances”, Theory Probab. Appl., 22:1 (1977), 124–128
V. N. Tutubalin, “A local limit theorem for products of random matrices”, Theory Probab. Appl., 22:2 (1978), 203–214
S. V. Rezničenko, “The structure of the fundamental matrix of a system of coupled-mode equations”, Theory Probab. Appl., 22:2 (1978), 311–325
Citation in format AMSBIB
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