Nicolai Haydn (University of Southern California)

A Central Limit Theorem for maps that are $(\phi,f)$ mixing.

Abstract. We prove that the Central Limit Theorem applies to the log of the measure of cylindersets for measures that are $(\phi,f)$-mixing. We approximate the measure of small cylinders by products of smaller cylinders and use the mixing property to show that in this way we get `nearly independent' random variables. Moreover, we show that the variance obtained from the variance of the information function and the entropy of joins. As a corollary we prove that the repeat time satisfies a CLT. This result involves the exponential law of the limiting distribution of returns to cylinder sets. Previously such results had been shown for Gibbs measures where the decay of correlations was used to obtain independence in the limit.