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Concentration inequalities for sequential dynamical systems of the unit interval

Published online by Cambridge University Press:  01 June 2015

ROMAIN AIMINO  and
JÉRÔME ROUSSEAU
ROMAIN AIMINO
Affiliation:
Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma, Italy email aimino@mat.uniroma2.it
JÉRÔME ROUSSEAU
Affiliation:
Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, BA, Brazil email jerome.rousseau@ufba.br
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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 $\unicode[STIX]{x1D6FD}$-transformations, with all $\unicode[STIX]{x1D6FD}$ lying in a neighborhood of a fixed $\unicode[STIX]{x1D6FD}_{\star }>1$, and systems satisfying a covering-type assumption.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 8 , December 2016 , pp. 2384 - 2407
Copyright
© Cambridge University Press, 2015 

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