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Perturbations of random matrix products in a reducible case

Published online by Cambridge University Press:  19 September 2008

Yuri Kifer
Affiliation:
Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel
Eric Slud
Affiliation:
Department of Mathematics, University of Maryland, College Park, Mary land 20742, USA
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Abstract

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It is known that for any sequence X1, X2…, of identically distributed independent random matrices with a common distribution μ. the limit

exists with probability 1. We study some conditions under which Λ(μk)→Λ(μ) provided μk → μ in the weak sense.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1982

References

REFERENCES

[1]Billingsley, P.. Convergence of Probability Measures. New York: John Wiley, 1968.Google Scholar
[2]Borel, A.. Linear Algebraic Groups. New York: W. A. Benjamin, 1969.Google Scholar
[3]Cohen, J.. Ergodic theorems in demography. Bull. Amer. Math. Soc. (New Series)1 (1979) 275295.CrossRefGoogle Scholar
[4]Doob, J. L.. Stochastic Processes. New York: John Wiley, 1953.Google Scholar
[5]Dudley, R. M.. Distances of probability measures and random variables. Ann. Math. Statist. 39 (1968) 15631572.CrossRefGoogle Scholar
[6]Furstenberg, H.Kesten, H.. Products of random matrices. Ann. Math. Statist. 31 (1960) 457469.CrossRefGoogle Scholar
[7]Furstenberg, H.. Non-commuting random products. Trans. Amer. Math. Soc. 108 (1963) 377428.CrossRefGoogle Scholar
[8]Ishii, K. & Matsuda, H.. Localization of normal modes and energy transport in the disordered harmonic chain. Progr. Theor. Phys. Suppl. 45 (1970) 5686.Google Scholar
[9]Kifer, Y.. Perturbations of random matrix products. Z. Wahrscheinlickkeitstheorie und verw. Gebiete. 61 (1982) 8395.CrossRefGoogle Scholar
[10]Oseledec, V. I.. A multiplicative ergodic theorem, Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19 (1968) 197221.Google Scholar
[11]Ruelle, D.. Analyticity properties of the characteristic exponents of random matrix products. Adv. in Math. 32 (1979) 6880.CrossRefGoogle Scholar
[12]Slud, E.. Products of independent randomly perturbed matrices. Ergodic Theory & Dynamical Systems, Vol. II. ed. Katok, A.. Boston: Birkh¨auser, 1982, 185192.CrossRefGoogle Scholar