Large deviation principles for periodic points of the Dyck shift
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913743616606208 |
|---|---|
| author | Takahasi, Hiroki |
| author_facet | Takahasi, Hiroki |
| contents | We investigate periodic points of the Dyck shift from the viewpoint of large deviations. We establish the level-2 Large Deviation Principle with the rate function given in terms of Kolmogorov-Sinai entropies of shift-invariant Borel probability measures. Unlike topologically mixing Markov shifts, the level-2 rate function is non-convex and level-1 rate functions are superpositions of two convex continuous functions. Using the thermodynamic formalism, we show the analyticity of level-1 rate functions in some relevant cases. We display a non-convex level-1 rate function with a non-differentiable point in the interior of its effective domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14164 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large deviation principles for periodic points of the Dyck shift Takahasi, Hiroki Dynamical Systems Probability We investigate periodic points of the Dyck shift from the viewpoint of large deviations. We establish the level-2 Large Deviation Principle with the rate function given in terms of Kolmogorov-Sinai entropies of shift-invariant Borel probability measures. Unlike topologically mixing Markov shifts, the level-2 rate function is non-convex and level-1 rate functions are superpositions of two convex continuous functions. Using the thermodynamic formalism, we show the analyticity of level-1 rate functions in some relevant cases. We display a non-convex level-1 rate function with a non-differentiable point in the interior of its effective domain. |
| title | Large deviation principles for periodic points of the Dyck shift |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2503.14164 |