AUTHOR=Poghosyan Ruben , Saakian David B. TITLE=Infinite Series of Singularities in the Correlated Random Matrices Product JOURNAL=Frontiers in Physics VOLUME=9 YEAR=2021 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.678805 DOI=10.3389/fphy.2021.678805 ISSN=2296-424X ABSTRACT=

We consider the product of a large number of two 2 × 2 matrices chosen randomly (with some correlation): at any round there are transition probabilities for the matrix type, depending on the choice at previous round. Previously, a functional equation has been derived to calculate such a random product of matrices. Here, we identify the phase structure of the problem with exact expressions for the transition points separating “localized” and “ergodic” regimes. We demonstrate that the latter regime develops through a formation of an infinite series of singularities in the steady-state distribution of vectors that results from the action of the random product of matrices on an initial vector.