Hitting Times and Positions in Rare Events

2018/10/24 by Roland Zweimüller, Zweimüller, Roland · 1 citation
Physics and Astronomy · #28D05 #Complex Network Analysis Techniques #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1810.10381

openalex publication_date 2018/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish abstract limit theorems which provide sufficient conditions for a sequence (A_l) of rare events in an ergodic probability preserving dynamical system to exhibit Poisson asymptotics, and for the consecutive positions inside the A_l to be asymptotically iid (spatiotemporal Poisson limits). The limit theorems only use information on what happens to A_l before some time τ_l which is of order o(1/μ(A_l)). In particular, no assumptions on the asymptotic behavior of the system akin to classical mixing conditions are used. We also discuss some general questions about the asymptotic behaviour of spatial and spatiotemporal processes, and illustrate our results in a setup of simple prototypical systems.

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