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A concentration inequality for interval maps with an indifferent fixed point

Published online by Cambridge University Press:  01 August 2009

J.-R. CHAZOTTES ,
P. COLLET ,
F. REDIG  and
E. VERBITSKIY
J.-R. CHAZOTTES
Affiliation:
Centre de Physique Théorique, CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex, France (email: chazottes@cpht.polytechnique.fr, collet@cpht.polytechnique.fr)
P. COLLET
Affiliation:
Centre de Physique Théorique, CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex, France (email: chazottes@cpht.polytechnique.fr, collet@cpht.polytechnique.fr)
F. REDIG
Affiliation:
Mathematisch Instituut Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands (email: redig@math.leidenuniv.nl)
E. VERBITSKIY
Affiliation:
Philips Research, HTC 36 (M/S 2), 5656 AE Eindhoven, The Netherlands (email: evgeny.verbitskiy@philips.com)
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Abstract

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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→ℝ, which are separately Lipschitz. The proof is based on coupling and decay of correlation properties of the map. We also present applications of this inequality to the almost-sure central limit theorem, the kernel density estimation, the empirical measure and the periodogram.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 4 , August 2009 , pp. 1097 - 1117
Copyright
Copyright © Cambridge University Press 2009

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