Local limit theorems for hitting times and return times of small sets

2023/12/22 by Auer, Max, Zweimüller, Roland
#37A05 #37E05 #60F05 #60G10 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.14581

Abstract

We establish abstract local limit theorems for hitting times and return-times of suitable sequences (A_l) of asymptotically rare events in ergodic probability preserving dynamical systems, including versions for tuples of consecutive times and positions of the hits. These results are shown to apply in the setup of Gibbs-Markov systems.

Related

• Hitting Times and Positions in Rare Events
• Hitting-time Limits for some Exceptional Rare Events of Ergodic Maps
• Return- and hitting-time distributions of small sets in infinite measure preserving systems
• Hitting and return times in ergodic dynamical systems
• Asymptotics for hitting times