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Products of Independent Randomly Perturbed Matrices

Chapter
Part of the Progress in Mathematics book series (PM, volume 21)

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.

Keywords

Unique Density Strong Markov Property Random Product Reducible Subgroup Unique Invariant Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Furstenberg, H., “Non-commuting random products,” T.A.M.S. (1963), 377-428.Google Scholar
  2. Furstenberg, H. and H. Kesten, “Products of random matrices,” Ann. Math. Stat. 31. (1960), 457–469.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Kingman, J. F. C., “Subadditive ergodic theory,” Ann. Prob. 1 (1973), 883–899.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1982

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA

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