Repetition times for Gibbsian sources
Pierre Collet, Antonio Galves, Bernard Schmitt · Nonlinearity · 1999
In this paper we consider the class of stochastic stationary sources induced by onedimensional Gibbs states, with Hölder 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.