Abstract
The almost sure limit π1 of n−1log∥AnAn−1...A1∥, proved by Furstenberg and Kesten (1960) to exist for strictly stationary random sequences of k × k matrices Ai, is shown to be stable under small independent orthogonal perturbations of Ai when the Ai are independent identically distributed matrices which almost surely commute and take on only finitely many values.
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References
Furstenberg, H., “Non-commuting random products,” T.A.M.S. (1963), 377-428.
Furstenberg, H. and H. Kesten, “Products of random matrices,” Ann. Math. Stat. 31. (1960), 457–469.
Kingman, J. F. C., “Subadditive ergodic theory,” Ann. Prob. 1 (1973), 883–899.
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© 1982 Springer Science+Business Media New York
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Slud, E.V. (1982). Products of Independent Randomly Perturbed Matrices. In: Katok, A. (eds) Ergodic Theory and Dynamical Systems II. Progress in Mathematics, vol 21. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-2689-0_6
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DOI: https://doi.org/10.1007/978-1-4899-2689-0_6
Publisher Name: Birkhäuser, Boston, MA
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