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Article Dans Une Revue Mathematical Physics, Analysis and Geometry Année : 2019

Regular expansion for the characteristic exponent of a product of 2 × 2 random matrices

Résumé

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 $\epsilon >0$ 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 $\epsilon$ 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.

Dates et versions

hal-01849549 , version 1 (26-07-2018)

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Benjamin Havret. Regular expansion for the characteristic exponent of a product of 2 × 2 random matrices. Mathematical Physics, Analysis and Geometry, 2019, 22 (2), ⟨10.1007/s11040-019-9312-x⟩. ⟨hal-01849549⟩
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