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

Raquel Couto; Ana Cristina Freitas; Jorge Freitas; Mike Todd

doi:10.1016/j.physd.2025.134989

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

Raquel Couto, Ana Cristina Freitas, Jorge Freitas, Mike Todd

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	134989
Journal	Physica D: Nonlinear Phenomena
Volume	483
Early online date	28 Oct 2025
DOIs	https://doi.org/10.1016/j.physd.2025.134989
Publication status	E-pub ahead of print - 28 Oct 2025

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Couto_2025_PD_Functional-limit-theorem_CC
Copyright © 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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AB - 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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A functional limit theorem for a dynamical system with an observable maximised on a Cantor set

Abstract

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