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 → 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.
    Original languageEnglish
    Pages (from-to)1097-1117
    Number of pages21
    JournalErgodic Theory and Dynamical Systems
    Volume29
    Issue number4
    DOIs
    Publication statusPublished - Aug-2009

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