Introduction to weak Pinsker filtrations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912303532736512 |
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| author | Benzoni, Séverin |
| author_facet | Benzoni, Séverin |
| contents | We introduce the so-called weak Pinsker dynamical filtrations, whose existence in any ergodic system follows from the universality of the weak Pinsker property, recently proved by Austin. These dynamical filtrations appear as a potential tool to describe and classify positive entropy systems. We explore the links between the asymptotic structure of weak Pinsker filtrations and the properties of the underlying dynamical system. A central question is whether, on a given system, the structure of weak Pinsker filtrations is unique up to isomorphism. We give a partial answer, in the case where the underlying system is Bernoulli. We conclude our work by giving two explicit examples of weak Pinsker filtrations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_00681 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Introduction to weak Pinsker filtrations Benzoni, Séverin Dynamical Systems Probability We introduce the so-called weak Pinsker dynamical filtrations, whose existence in any ergodic system follows from the universality of the weak Pinsker property, recently proved by Austin. These dynamical filtrations appear as a potential tool to describe and classify positive entropy systems. We explore the links between the asymptotic structure of weak Pinsker filtrations and the properties of the underlying dynamical system. A central question is whether, on a given system, the structure of weak Pinsker filtrations is unique up to isomorphism. We give a partial answer, in the case where the underlying system is Bernoulli. We conclude our work by giving two explicit examples of weak Pinsker filtrations. |
| title | Introduction to weak Pinsker filtrations |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2504.00681 |