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Products of random 2 £ 2 matrices exhibit Gaussian fluctuations around almost surely convergent Lyapunov exponents. In this paper, the distribution of the random matrices is supported by a small neighbourhood of order l . 0 of the identity matrix. The Lyapunov exponent and the variance of the Gaussian fluctuations are calculated perturbatively in l and this requires a detailed analysis of the associated random dynamical system on the unit circle and its invariant measure. The result applies to anomalies and band edges of one-dimensional random Schrödinger operators.

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