A concentration inequality for interval maps with an indifferent fixed point

Details A concentration inequality for interval maps with an indifferent fixed point A concentration inequality for interval maps with an indifferent fixed point

2008-01-23

arxiv.org/abs/0801.3567v1

Published in Ergod. Th. Dynam. Sys. vol. 29 (2009)

Mathematics

Dynamical Systems

26 pages, submitted

Scientific paper

For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of $n$ variables $K:[0,1]^n\to\R$ which are componentwise Lipschitz. The proof is based on coupling and decay of correlation properties of the map. We then give various applications of this inequality to the almost-sure central limit theorem, the kernel density estimation, the empirical measure and the periodogram.

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