Concentration inequalities for sequential dynamical systems of the unit interval

J\'er\^ome Rousseau; Romain Aimino

Concentration inequalities for sequential dynamical systems of the unit interval

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arxiv 1406.3213 v3 pith:MQRA2W6B submitted 2014-06-12 math.DS math.PR

Concentration inequalities for sequential dynamical systems of the unit interval

Romain Aimino , J\'er\^ome Rousseau This is my paper

classification math.DS math.PR

keywords betasystemsconcentrationdynamicalintervalsequentialunitassumption

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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.

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