Predictability, entropy and information of infinite transformations
| Autor: | Jon Aaronson, Kyewon Koh Park |
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| Rok vydání: | 2007 |
| Předmět: | |
| DOI: | 10.48550/arxiv.0705.2148 |
| Popis: | We show that a certain type of quasi finite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving transformation which is not quasi finite; and consider distribution asymptotics of information showing that e.g. for Boole's transformation, information is asymptotically mod-normal with square root normalization. Lastly we see that certain ergodic, probability preserving transformations with zero entropy have analogous properties and consequently entropy dimension of at most 1/2. Comment: typos corrected, clarifications added, unproved result removed |
| Databáze: | OpenAIRE |
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