Abstract : To every product of 2×22×2 matrices, there corresponds a one-dimensional Schr\ »{o}dinger equation whose potential consists of generalised point scatterers. Products of {\em random} matrices are obtained by making these interactions and their positions random. We exhibit a simple one-dimensional quantum model corresponding to the most general product of matrices in SL(2,R)SL(2,R). We use this correspondence to find new examples of products of random matrices for which the invariant measure can be expressed in simple analytical terms.
Alain Comtet 1, 2 Christophe Texier 2, 3 Yves Tourigny 4
1 IHP – Institut Henri Poincaré
2 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
3 LPS – Laboratoire de Physique des Solides
4 School of Mathematics [Bristol]
