Email this article Asymptotics of the Partition of the Cube into Weyl Simplices and an Encoding of a Bernoulli Scheme
- Authors: Vershik A.M.1,2,3
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Affiliations:
- St. Petersburg Department of Steklov Institute of Mathematics, Russian Academy of Sciences
- St. Petersburg State University
- Institute for Information Transmission Problems, Russian Academy of Sciences
- Issue: Vol 53, No 2 (2019)
- Pages: 86-101
- Section: Article
- URL: https://journals.rcsi.science/0016-2663/article/view/234565
- DOI: https://doi.org/10.1134/S0016266319020023
- ID: 234565
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Abstract
We suggest a combinatorial method for encoding continuous symbolic dynamical systems. We transform a continuous phase space, the infinite-dimensional cube, into the path space of a tree, and the shift corresponds to a transformation which we called “transfer.” The central problem is that of distinguishability: does the encoding distinguishes between almost all points of the space? The main result says that the encoding by means of the partition of the cube into Weyl simplices has this property.
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About the authors
A. M. Vershik
St. Petersburg Department of Steklov Institute of Mathematics, Russian Academy of Sciences; St. Petersburg State University; Institute for Information Transmission Problems, Russian Academy of Sciences
Email: funan@pleiadesonline.com
Russian Federation, St. Petersburg; St. Petersburg; Moscow
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