Repetition times for Gibbsian sources

1999

In this paper we consider the class of stochastic stationary sources induced by one-dimensional Gibbs states, with Holder continuous potentials. We show that the time elapsed before the source repeats its first n symbols, when suitably renormalized, converges in law either to a log-normal distribution or to a finite mixture of exponential random variables. In the first case we also prove a large deviation result.