Email this article Limiting Curves for Polynomial Adic Systems
- Authors: Minabutdinov A.R.1
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Affiliations:
- National Research University Higher School of Economics, Department of Applied Mathematics and Business Informatics
- Issue: Vol 224, No 2 (2017)
- Pages: 286-303
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239558
- DOI: https://doi.org/10.1007/s10958-017-3415-3
- ID: 239558
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Abstract
We prove the existence of and describe limiting curves resulting from deviations in the partial sums in the ergodic theorem for cylinder functions and polynomial adic systems. For a general ergodic measure-preserving transformation and a summable function, we give a necessary condition for a limiting curve to exist. Our work generalizes results by É. Janvresse, T. de la Rue, and Y. Velenik and answers several questions from their work.
About the authors
A. R. Minabutdinov
National Research University Higher School of Economics, Department of Applied Mathematics and Business Informatics
Author for correspondence.
Email: aminabutdinov@hse.ru
Russian Federation, St. Petersburg
