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arXiv · 1502.07845

Gaussian fluctuations of products of random matrices distributed close to the identity

Maxim Drabkin·Hermann Schulz-Baldes
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Abstract

Products of random $2\times 2$ matrices exhibit Gaussian fluctuations around almost surely convergent Lyapunov exponents. In this paper, the distribution of the random matrices is supported by a small neighborhood of order $\lambda>0$ of the identity matrix. The Lyapunov exponent and the variance of the Gaussian fluctuations are calculated perturbatively in $\lambda$ 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 Schr\"odinger operators.

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Maxim Drabkin, Hermann Schulz-Baldes. 2015-02-27. Gaussian fluctuations of products of random matrices distributed close to the identity. https://arxiv.org/abs/1502.07845

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