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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.05698 |
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| _version_ | 1866915718786711552 |
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| author | Gröger, Maik Jaerisch, Johannes Kesseböhmer, Marc |
| author_facet | Gröger, Maik Jaerisch, Johannes Kesseböhmer, Marc |
| contents | We study $\mathbb Z$- and $\mathbb N$-extensions of interval maps with at most countably many full branches modelling one-dimensional random walks without and with a reflective boundary. We analyse the associated Gurevich pressure and explore the relations governing these two cases. For such extensions, we obtain variational formulae for the Gurevich pressure that depend only on the base system. As a consequence, we characterise the systems with a dimension gap and, in the presence of a reflective boundary, provide general conditions in terms of asymptotic covariances for a second order phase transition. As a by-product, we derive a variational formula for the spectral radius of infinite Hessenberg matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05698 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dimension gap and phase transition for one-dimensional random walks with reflective boundary Gröger, Maik Jaerisch, Johannes Kesseböhmer, Marc Dynamical Systems Mathematical Physics Probability 37E05, 37D35, 28A80, 60J10 We study $\mathbb Z$- and $\mathbb N$-extensions of interval maps with at most countably many full branches modelling one-dimensional random walks without and with a reflective boundary. We analyse the associated Gurevich pressure and explore the relations governing these two cases. For such extensions, we obtain variational formulae for the Gurevich pressure that depend only on the base system. As a consequence, we characterise the systems with a dimension gap and, in the presence of a reflective boundary, provide general conditions in terms of asymptotic covariances for a second order phase transition. As a by-product, we derive a variational formula for the spectral radius of infinite Hessenberg matrices. |
| title | Dimension gap and phase transition for one-dimensional random walks with reflective boundary |
| topic | Dynamical Systems Mathematical Physics Probability 37E05, 37D35, 28A80, 60J10 |
| url | https://arxiv.org/abs/2601.05698 |