Asymptotic Randomization of Sofic Shifts by Linear Cellular Automata
| dc.creator | Pivato, Marcus | |
| dc.creator | Yassawi, Reem | |
| dc.date | 2003-06-08 | |
| dc.date | 2006-04-13 | |
| dc.date.accessioned | 2026-07-07T06:35:39Z | |
| dc.date.available | 2026-07-07T06:35:39Z | |
| dc.description | Let M=Z^D be a D-dimensional lattice, and let A be an abelian group. A^M is then a compact abelian group; a `linear cellular automaton' (LCA) is a topological group endomorphism Φ:A^M --> A^M that commutes with all shift maps. Suppose μis a probability measure on A^M whose support is a subshift of finite type or sofic shift. We provide sufficient conditions (on Φand μ) under which Φ`asymptotically randomizes' μ, meaning that wk*lim_{J\ni j --> oo} Φ^j μ= η, where ηis the Haar measure on A^M, and J has Cesaro density 1. In the case when Φ=1+σ, we provide a condition on μthat is both necessary and sufficient. We then use this to construct an example of a zero-entropy measure which is asymptotically randomized by 1+σ(all previously known examples had positive entropy). | |
| dc.description | 24 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0306136 | |
| dc.identifier | http://arxiv.org/abs/math/0306136 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99858 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37B15 (Primary); 37A50 (Secondary) | |
| dc.title | Asymptotic Randomization of Sofic Shifts by Linear Cellular Automata | |
| dc.type | text |