Laws of Rare Events for Deterministic and Random Dynamical Systems

Hale Aytaç (1, 2, 3) , Jorge Milhazes Freitas (2) , Sandro Vaienti (3, 1)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CMUP - Centro de Matemática - Universidade do Porto
3 CPT - Ex E7 Systèmes dynamiques et théorie ergodique

The object of this paper is twofold. From one side we study the dichotomy, in terms of the Extremal Index of the possible Extreme Value Laws, when the rare events are centred around periodic or non periodic points. Then we build a general theory of Extreme Value Laws for randomly perturbed dynamical systems. We also address, in both situations, the convergence of Rare Events Point Processes. Decay of correlations against L 1 observables will play a central role in our investigations.

Domaines: Systèmes dynamiques [math.DS]

Hale Aytaç, Jorge Milhazes Freitas, Sandro Vaienti. Laws of Rare Events for Deterministic and Random Dynamical Systems. Transactions of the American Mathematical Society, 2015, 367, pp.8229-8278. ⟨10.1090/S0002–9947–2014–06300–9⟩. ⟨hal-01126671⟩