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The largest Lyapunov exponent for random matrices and directed polymers in a random environment. (English) Zbl 0673.60066
The paper establishes bounds for the largest Lyapunov exponent of random matrix products with matrices being either d-dimensional Laplacians with random entries or symplectic matrices which arise in the study of d- dimensional lattices of coupled, nonlinear oscillators. The method uses the expression for the largest Lyapunov exponent via a random walk in a random environment.
Reviewer: Y.Kifer

MSC:
60H25 Random operators and equations (aspects of stochastic analysis)
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
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