Products of Independent Randomly Perturbed Matrices
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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.
KeywordsUnique Density Strong Markov Property Random Product Reducible Subgroup Unique Invariant Measure
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- Furstenberg, H., “Non-commuting random products,” T.A.M.S. (1963), 377-428.Google Scholar