AUTHOR=Poghosyan Ruben , Saakian David B. 

TITLE=Infinite Series of Singularities in the Correlated Random Matrices Product

JOURNAL=Frontiers in Physics

VOLUME=Volume 9 - 2021

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.