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A concentration inequality for interval maps with an indifferent fixed point

Chazottes, J-R., Collet, P., Redig, F. & Verbitskiy, E., Aug-2009, In : Ergodic Theory and Dynamical Systems. 29, 4, p. 1097-1117 21 p.

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  • A concentration inequality for interval maps withan indifferent fixed point

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DOI

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
Publication statusPublished - Aug-2009

ID: 14403719