A functional limit theorem for a dynamical system with an observable maximised on a Cantor set
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918292981022720 |
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| author | Couto, Raquel Freitas, Ana Cristina Moreira Freitas, Jorge Milhazes Todd, Mike |
| author_facet | Couto, Raquel Freitas, Ana Cristina Moreira Freitas, Jorge Milhazes Todd, Mike |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A functional limit theorem for a dynamical system with an observable maximised on a Cantor set Couto, Raquel Freitas, Ana Cristina Moreira Freitas, Jorge Milhazes Todd, Mike Dynamical Systems Probability 37A25, 37A50, 37B20, 60F17, 60G55, 60G70 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. |
| title | A functional limit theorem for a dynamical system with an observable maximised on a Cantor set |
| topic | Dynamical Systems Probability 37A25, 37A50, 37B20, 60F17, 60G55, 60G70 |
| url | https://arxiv.org/abs/2504.12534 |