Recurrence, Short Correlations and the Golden Number

We consider a stochastic process with the weakest mixing condition: the so called $\alpha$. For \emph{any} fixed $n$-string we prove:(1) The hitting time has approximately exponential law.(2) The return time has approximately a convex combination between a Dirac measure at the origin and an exponential law.In both cases the parameter of the exponential law is $\lambda(A)IP(A)$ where $IP(A)$ is the measure of the string and $\lambda(A)$ is the short correlation function of the string with itself. Also, we show that the weight of the convex combination is a approximately $\lambda(A)$. We describe the autocorrelation function. Our results hold when the rate $\alpha$ decays polinomially fast with power larger than the golden number.