期刊
ISRAEL JOURNAL OF MATHEMATICS
卷 139, 期 -, 页码 29-65出版社
MAGNES PRESS
DOI: 10.1007/BF02787541
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We generalize a method developed by Sarig to obtain polynomial lower bounds for correlation functions for maps with a countable Markov partition. A consequence is that LS Young's estimates on towers are always optimal. Moreover, we show that, for functions with zero average, the decay rate is better, gaining a factor 1/n. This implies a Central Limit Theorem in contexts where it was not expected, e.g., x + Cx(1+alpha) with 1/2 less than or equal to alpha < 1. The method is based on a general result on renewal sequences of operators, and gives an asymptotic estimate up to any precision of such operators.
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