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Teoriya Veroyatnostei i ee Primeneniya, 1970, Volume 15, Issue 2, Pages 291–303 (Mi tvp1791)  
This article is cited in 9 scientific papers (total in 9 papers)

A multiwave transmission line with random non-homogeneities and a Brownian movement in Siegel's circle

M. H. Zakhar-Itkin

Moscow
Full-text PDF (769 kB) Citations (9)
Abstract: A multiwave transmission line without loses is considered. After a similarity transformation of the matrix coefficient of reflection, it becomes a point of the classical matrix, domain of the first kind, in other words, Siegel's circle.
A transmission along the transmission line leads to a linear fractional transformation of Siegel's circle onto itself. A diffusion equation for a random walk corresponding to these transformations in Siegel's circle is obtained. The invariance of the diffusuion equation enables to study the statistics of the random distance from zero matrix to a walkingspoint of Siegel's circle.
Received: 27.03.1969
English version:
Theory of Probability and its Applications, 1970, Volume 15, Issue 2, Pages 282–294
DOI: https://doi.org/10.1137/1115033
Bibliographic databases:
Language: Russian
Citation: M. H. Zakhar-Itkin, “A multiwave transmission line with random non-homogeneities and a Brownian movement in Siegel's circle”, Teor. Veroyatnost. i Primenen., 15:2 (1970), 291–303; Theory Probab. Appl., 15:2 (1970), 282–294
Citation in format AMSBIB
\Bibitem{Zak70}
\by M.~H.~Zakhar-Itkin
\paper A~multiwave transmission line with random non-homogeneities and a~Brownian movement in Siegel's circle
\jour Teor. Veroyatnost. i Primenen.
\yr 1970
\vol 15
\issue 2
\pages 291--303
\mathnet{http://mi.mathnet.ru/tvp1791}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=269193}
\zmath{https://zbmath.org/?q=an:0206.19102}
\transl
\jour Theory Probab. Appl.
\yr 1970
\vol 15
\issue 2
\pages 282--294
\crossref{https://doi.org/10.1137/1115033}
Linking options:
  • https://www.mathnet.ru/eng/tvp1791
  • https://www.mathnet.ru/eng/tvp/v15/i2/p291
    • This publication is cited in the following 9 articles:
    1. Bernard Souillard, NATO ASI Series, 120, Chaotic Behavior in Quantum Systems, 1985, 1  crossref
    2. Bernard Souillard, “Electrons in random and almost-periodic potentials”, Physics Reports, 103:1-4 (1984), 41  crossref
    3. S. V. Rezničenko, “Radio waveguides and diffusion processes on differentiable manifolds”, Theory Probab. Appl., 21:2 (1977), 357–369  mathnet  mathnet  crossref
    4. M. H. Zakhar-Itkin, “The matrix Riccati differential equation and the semi-group of linear fractional transformations”, Russian Math. Surveys, 28:3 (1973), 89–131  mathnet  crossref  mathscinet  zmath
    5. M. H. Zakhar-Itkin, “On Statistics of the Reflection Coefficient of a Dissipative Multiwave Transmission Line with Random Section Lengths”, Theory Probab. Appl., 18:2 (1973), 281–294  mathnet  mathnet  crossref
    6. R. Burridge, G. Papanicolaou, “The geometry of coupled mode propagation in one‐dimensional random media”, Comm Pure Appl Math, 25:6 (1972), 715  crossref
    7. V. N. Tutubalin, “A representation of random matrices in orispherical coordinates and its application to telegraph equations”, Theory Probab. Appl., 17:2 (1973), 255–268  mathnet  mathnet  crossref
    8. M. H. Zahar-Itkin, “Multimode transmission line noises and summation of random vectors”, Theory Probab. Appl., 16:3 (1971), 556–559  mathnet  mathnet  crossref
    9. V. N. Tutubalin, “Multimode waveguides and probability distributions on a symplectic group”, Theory Probab. Appl., 16:4 (1971), 631–642  mathnet  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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