A generalized central limit theorem in infinite ergodic theory

@article{Thomine2014AGC,
  title={A generalized central limit theorem in infinite ergodic theory},
  author={Damien Thomine},
  journal={Probability Theory and Related Fields},
  year={2014},
  volume={158},
  pages={597-636}
}
We prove a generalized central limit theorem for dynamical systems with an infinite ergodic measure which induce a Gibbs–Markov map on some subset, provided the return time to this subset has regularly varying tails. We adapt a method designed by Csáki and Földes for observables of random walks to show that the partial sums of some functions of the system—the return time and the observable—are asymptotically independent. Some applications to random walks and Pomeau–Manneville maps are discussed… CONTINUE READING