Support stability of maximizing measures for shifts of finite type
| Autor: | Anthony Quas, Jason Siefken, Juliano S. Gonschorowski |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Applied Mathematics General Mathematics 010102 general mathematics Symbolic dynamics Context (language use) Subshift of finite type 01 natural sciences Stability (probability) 0103 physical sciences Ergodic theory Penalty method 010307 mathematical physics 0101 mathematics Invariant (mathematics) Probability measure Mathematics |
| Zdroj: | Ergodic Theory and Dynamical Systems. 41:869-880 |
| ISSN: | 1469-4417 0143-3857 |
| Popis: | This paper establishes a fundamental difference between $\mathbb{Z}$ subshifts of finite type and $\mathbb{Z}^{2}$ subshifts of finite type in the context of ergodic optimization. Specifically, we consider a subshift of finite type $X$ as a subset of a full shift $F$. We then introduce a natural penalty function $f$, defined on $F$, which is 0 if the local configuration near the origin is legal and $-1$ otherwise. We show that in the case of $\mathbb{Z}$ subshifts, for all sufficiently small perturbations, $g$, of $f$, the $g$-maximizing invariant probability measures are supported on $X$ (that is, the set $X$ is stably maximized by $f$). However, in the two-dimensional case, we show that the well-known Robinson tiling fails to have this property: there exist arbitrarily small perturbations, $g$, of $f$ for which the $g$-maximizing invariant probability measures are supported on $F\setminus X$. |
| Databáze: | OpenAIRE |
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