Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.22742 |
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Sommario:
- In this paper I study properties of the generators $\triangle_γ$ of non-local Dirichlet forms $\mathcal{E}^μ_γ$ on ultrametric spaces which are the path space of simple stationary Bratteli diagrams. The measures used to define the Dirichlet forms are taken to be the Gibbs measures $μ_ψ$ associated to Hölder continuous potentials $ψ$ for one-sided shifts. I also define a cohomology $H_{lc}(X_B)$ for $X_B$ which can be seen as dual to the homology of Bowen and Franks. Besides studying spectral properties of $\triangle_γ$, I show that for $γ$ large enough (with sharp bounds depending on the diagram and the measure theoretic entropy $h_{μ_ψ}$ of $μ_ψ$) there is a unique $\mathcal{E}^μ_γ$-minimizing representative of any class $c\in H_{lc}(X_B)$.