Anomalous time-scaling of extreme events in infinite systems and Birkhoff sums of infinite observables
We establish quantitative results for the statistical behaviour of infinite systems. We consider two kinds of infinite system: i) a conservative dynamical system (f, X, µ) preserving a σ-finite measure µ such that µ(X) = ∞; ii) the case where µ is a probability measure but we consider the statistical behaviour of an observable φ: X → [0, ∞) which is non-integrable: R φ dµ = ∞. In the first part of
