Birkhoff sum convergence of Fréchet observables to stable laws for Gibbs-Markov systems and applications

An Chen, Matthew Nicol, Andrew Török

We use a Poisson point process approach to prove distributional convergence to a stable law for non square-integrable observables $\varphi :[0,1]\to R$, mostly of the form $ϕ(x) = d(x,x_…