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arXiv · 1804.06166

Regular expansion for the characteristic exponent of a product of $2 \times 2$ random matrices

Benjamin Havret
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Abstract

We consider a product of $2 \times 2$ random matrices which appears in the physics literature in the analysis of some 1D disordered models. These matrices depend on a parameter $ε>0$ and on a positive random variable $Z$. Derrida and Hilhorst (J Phys A 16:2641, 1983, §3) predict that the corresponding characteristic exponent has a regular expansion with respect to $ε$ up to --- and not further --- an order determined by the distribution of $Z$. We give a rigorous proof of that statement. We also study the singular term which breaks that expansion.

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Benjamin Havret. 2018-12-21. Regular expansion for the characteristic exponent of a product of $2 \times 2$ random matrices. https://doi.org/10.1007/s11040-019-9312-x

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