On Mealy–Moore coding and images of Markov measures
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- by R. Grigorchuk, R. Kogan and Ya. Vorobets
- Trans. Moscow Math. Soc. 2021, 89-115
- DOI: https://doi.org/10.1090/mosc/314
- Published electronically: March 15, 2022
Abstract:
We study the images of the Markov measures under transformations generated by the Mealy automata. We find conditions under which the image measure is absolutely continuous or singular relative to the Markov measure. Also, we determine statistical properties of the image of a generic sequence.References
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Bibliographic Information
- R. Grigorchuk
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77840
- MR Author ID: 193739
- Email: grigorch@math.tamu.edu
- R. Kogan
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77840
- Email: romwell@gmail.com
- Ya. Vorobets
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77840
- Email: yvorobet@math.tamu.edu
- Published electronically: March 15, 2022
- Additional Notes: The first author gratefully acknowledges support from the Simons Foundation through Collaboration Grant #527814.
- © Copyright 2021 R. Grigorchuk, R. Kogan, Ya. Vorobets
- Journal: Trans. Moscow Math. Soc. 2021, 89-115
- MSC (2020): Primary 37A50, 37B10
- DOI: https://doi.org/10.1090/mosc/314
- MathSciNet review: 4397154