A functional limit theorem for a dynamical system with an observable maximised on a Cantor set

2025/04/16 by Raquel Couto, Ana Cristina Moreira Freitas, Couto, Raquel +5
Engineering · Mathematics · #37A25 #37A50 #37B20 #60F17 #60G55 #60G70 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #Probability (math.PR) #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.2504.12534

openalex publication_date 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider heavy-tailed observables maximised on a dynamically defined Cantor set and prove convergence of the associated point processes as well as functional limit theorems. The Cantor structure, and its connection to the dynamics, causes clustering of large observations: this is captured in the `decorations' on our point processes and functional limits, an application of the theory developed in a paper by the latter three authors.

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