Almost Sure Central Limit Theorems and the Erdös-Rényi law for Expanding Maps of the Interval

@inproceedings{Chazottes2008AlmostSC,
  title={Almost Sure Central Limit Theorems and the Erd{\"o}s-R{\'e}nyi law for Expanding Maps of the Interval},
  author={J.-R. Chazottes},
  year={2008}
}
For a large class of expanding maps of the interval, we prove that partial sums of Lipschitz observables satisfy an almost sure central limit theorem (ASCLT). In fact, we provide a rate of convergence in the Kantorovich distance. Maxima of partial sums are also shown to obey an ASCLT. The key-tool is an exponential inequality recently obtained. Then we establish (optimal) almost-sure convergence rates for the supremum of moving averages of Lipschitz observables (Erdös-Rényi type law). This is… CONTINUE READING

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