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arXiv · 0801.3567

A concentration inequality for interval maps with an indifferent fixed point

J. -R. Chazottes·P. Collet·F. Redig·E. Verbitskiy
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Abstract

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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J. -R. Chazottes, P. Collet, F. Redig, E. Verbitskiy. 2008-01-23. A concentration inequality for interval maps with an indifferent fixed point. https://arxiv.org/abs/0801.3567

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