Geodesic
A~multiwave transmission line with random non-homogeneities and a~Brownian movement in Siegel's circle
Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 2, pp. 291-303

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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. 
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     author = {M. H. Zakhar-Itkin},
     title = {A~multiwave transmission line with random non-homogeneities and {a~Brownian} movement in {Siegel's} circle},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {291--303},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_2_a8/}
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M. H. Zakhar-Itkin. A~multiwave transmission line with random non-homogeneities and a~Brownian movement in Siegel's circle. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 2, pp. 291-303. http://geodesic.mathdoc.fr/item/TVP_1970_15_2_a8/