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

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 $\epsilon >0$ 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.
Keywords :
Type de document :
Pré-publication, Document de travail
2018
Domaine :

https://hal.archives-ouvertes.fr/hal-01849549
Contributeur : Benjamin Havret <>
Soumis le : jeudi 26 juillet 2018 - 11:52:41
Dernière modification le : vendredi 4 janvier 2019 - 17:33:38

### Identifiants

• HAL Id : hal-01849549, version 1

### Citation

Benjamin Havret. Regular expansion for the characteristic exponent of a product of 2 × 2 random matrices. 2018. 〈hal-01849549〉

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