Spectral decomposition of contracting probabilistic dynamical systems

Abstract

We study probabilistic couplings of a finite class of linear contractions of the unit interval. For this reason we call these systems ‘contracting probabilistic dynamical systems’. The resulting system is a stationary Markov process with deterministic outcomes. Each outcome results from the application of one of the contractions. The selection of each contraction is conditioned probabilistically. We study these systems through the spectral properties of their corresponding sthocastic and Markov operators.