Repetition times for Gibbsian sources

In this paper we consider the class of stochastic stationary sources induce d by one-dimensional Gibbs states, with Holder continuous potentials, we sh ow that the time elapsed before the source repeats its first it symbols, wh en suitably renormalized, converges in law either to a log-normal distribut ion or to a finite mixture of exponential random variables. In the first ca se we also prove a large deviation result.