Geodesic
The evaluation of statistical characteristics of long waveguides in two-modes model
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 94-108

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The product of random independent matrices (of second order) is considered as an exact model of a long waveguide with two propagating modes. Two approximate methods for evaluation of statistical characteristics of such models are given: a diffusion approximation and a sort of the central limit theorem. The accuracy of these approximations is investigated by the Monte-Carlo simulation. Monte-Carlo experiments are found not to be statistically stable, but a certain agreement exists between the results of these experiments and the approximate methods given in this paper. 
@article{TVP_1973_18_1_a6,
     author = {T. V. Selezneva and V. N. Tutubalin},
     title = {The evaluation of statistical characteristics of long waveguides in two-modes model},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {94--108},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a6/}
}
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T. V. Selezneva; V. N. Tutubalin. The evaluation of statistical characteristics of long waveguides in two-modes model. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 94-108. http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a6/