On the simplicity of the spectrum of Lyapunov's characteristic indices of a~product of random matrices
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 1, pp. 115-128
Voir la notice de l'article provenant de la source Math-Net.Ru
It is proved that the spectrum of Lyapunov's characteristic indices of a product of random matrices [4] is simple when multipliers form a stationary Markov chain on the group $SL(m,R)$ and the transitional probability of a chain satisfies some regularity conditions. When multipliers are independent and their distribution is absolutely continuous with respect to the Haar's measure on $SL(m,R)$ the simplicity of the spectrum of the characteristic indiced is a well-known result proved by V. N. Tutubalin [2] and (in a less explicite form) by H. Furstenberg [1]. The method of proof in the present paper is based on the development of some ideas of H. Furstenberg in [1] and generalizes the method of representations used in [8] (see also [9]–[11])
@article{TVP_1983_28_1_a6,
author = {A. D. Vir{\cyrs}er},
title = {On the simplicity of the spectrum of {Lyapunov's} characteristic indices of a~product of random matrices},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {115--128},
publisher = {mathdoc},
volume = {28},
number = {1},
year = {1983},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a6/}
}
TY - JOUR AU - A. D. Virсer TI - On the simplicity of the spectrum of Lyapunov's characteristic indices of a~product of random matrices JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1983 SP - 115 EP - 128 VL - 28 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a6/ LA - ru ID - TVP_1983_28_1_a6 ER -
A. D. Virсer. On the simplicity of the spectrum of Lyapunov's characteristic indices of a~product of random matrices. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 1, pp. 115-128. http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a6/