2016/01/08 by Alain Comtet, Comtet, Alain, Yves Tourigny +1 · 1 citation
Computer Science · #15B52 #82B44 #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1601.01822
openalex publication_date 2016/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is an introduction to the theory of one-dimensional disordered systems and products of random matrices, confined to the 2 by 2 case. The notion of impurity model--- that is, a system in which the interactions are highly localised--- links the two themes and enables their study by elementary mathematical tools. After discussing the spectral theory of some impurity models, we state and illustrate Furstenberg's theorem, which gives sufficient conditions for the exponential growth of a product of independent, identically-distributed matrices.