Sharp Statistical Properties for a Family of Multidimensional NonMarkovian Nonconformal Intermittent Maps

Peyman Eslami , Ian Melbourne , Sandro Vaienti (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E7 Systèmes dynamiques : théories et applications

Intermittent maps of Pomeau-Manneville type are well-studied in one-dimension, and also in higher dimensions if the map happens to be Markov. In general, the nonconformality of multidimensional intermittent maps represents a challenge that up to now is only partially addressed. We show how to prove sharp polynomial bounds on decay of correlations for a class of multidimensional intermittent maps. In addition we show that the optimal results on statistical limit laws for one-dimensional intermittent maps hold also for the maps considered here. This includes the (functional) central limit theorem and local limit theorem, Berry-Esseen estimates, large deviation estimates, convergence to stable laws and L\'evy processes, and infinite measure mixing.

Domaines: Systèmes dynamiques [math.DS]

Peyman Eslami, Ian Melbourne, Sandro Vaienti. Sharp Statistical Properties for a Family of Multidimensional NonMarkovian Nonconformal Intermittent Maps. Advances in Mathematics, 2021, 388, ⟨10.1016/j.aim.2021.107853⟩. ⟨hal-03166966⟩