Concentration inequalities for sequential dynamical systems of the unit interval

Abstract

We prove a concentration inequality for sequential dynamical systems of the unit interval enjoying an exponential loss of memory in the BV norm, and we investigate several of its consequences. In particular, this covers compositions of $\beta$-transformations, with all $\beta$ lying in a neighborhood of a fixed ${\beta }_{\star }>1$ and systems satisfying a covering type assumption.