The Shannon–McMillan theorem for doubly stochastic operators
| Autor: | Bartosz Frej, Paulina Frej |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Discrete mathematics
Doubly stochastic matrix Pure mathematics Applied Mathematics General Physics and Astronomy Statistical and Nonlinear Physics Spectral theorem Operator theory Fourier integral operator Operator (computer programming) Operator norm Mathematical Physics Joint quantum entropy Entropy rate Mathematics |
| Zdroj: | Nonlinearity. 25:3453-3467 |
| ISSN: | 1361-6544 0951-7715 |
| DOI: | 10.1088/0951-7715/25/12/3453 |
| Popis: | In this paper we introduce and study an information function for doubly stochastic operators. This generalization of the notion, which is well known for classical dynamical systems, follows the earlier results on the entropy of operators by Downarowicz, Frej and Frej. As a main result we prove two versions of the Shannon–McMillan theorem for doubly stochastic operators, using the relations between the entropy of an operator and the entropy of a shift on a space of trajectories. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|