A functional limit theorem for a dynamical system with an observable maximised on a Cantor set
Dynamical Systems
2026-01-21 v2 Probability
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.
Cite
@article{arxiv.2504.12534,
title = {A functional limit theorem for a dynamical system with an observable maximised on a Cantor set},
author = {Raquel Couto and Ana Cristina Moreira Freitas and Jorge Milhazes Freitas and Mike Todd},
journal= {arXiv preprint arXiv:2504.12534},
year = {2026}
}