Differential transcendence and walks on self-similar graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908808657240064 |
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| author | Kahane, Yakob Mishna, Marni |
| author_facet | Kahane, Yakob Mishna, Marni |
| contents | Symmetrically self-similar graphs are an important type of fractal graph. Their Green functions satisfy order one iterative functional equations. We show when the branching number of a generating cell is two, either the graph is a star consisting of finitely many one-sided lines meeting at an origin vertex, in which case the Green function is algebraic, or the Green function is differentially transcendental over $\mathbb{C}(z)$. The proof strategy relies on a recent work of Di Vizio, Fernandes and Mishna. The result adds evidence to a conjecture of Krön and Teufl about the spectrum of this family of graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19316 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differential transcendence and walks on self-similar graphs Kahane, Yakob Mishna, Marni Combinatorics Probability 60C05, 34M15 Symmetrically self-similar graphs are an important type of fractal graph. Their Green functions satisfy order one iterative functional equations. We show when the branching number of a generating cell is two, either the graph is a star consisting of finitely many one-sided lines meeting at an origin vertex, in which case the Green function is algebraic, or the Green function is differentially transcendental over $\mathbb{C}(z)$. The proof strategy relies on a recent work of Di Vizio, Fernandes and Mishna. The result adds evidence to a conjecture of Krön and Teufl about the spectrum of this family of graphs. |
| title | Differential transcendence and walks on self-similar graphs |
| topic | Combinatorics Probability 60C05, 34M15 |
| url | https://arxiv.org/abs/2411.19316 |