Holder continuity of interfaces for scale-invariant Poisson stick soup
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918308330078208 |
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| author | Teixeira, Augusto Ungaretti, Daniel |
| author_facet | Teixeira, Augusto Ungaretti, Daniel |
| contents | We study the interface of covered and vacant sets in the subcritical phase of a scale-invariant Poisson stick soup on the plane. This model is a natural candidate for scaling limit of some planar models and has connections with long-range percolation on the plane with critical parameter $s=4$. We analyze a family of exploration paths on boxes and prove tightness for this family and Holder continuity for its limiting measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19546 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Holder continuity of interfaces for scale-invariant Poisson stick soup Teixeira, Augusto Ungaretti, Daniel Probability We study the interface of covered and vacant sets in the subcritical phase of a scale-invariant Poisson stick soup on the plane. This model is a natural candidate for scaling limit of some planar models and has connections with long-range percolation on the plane with critical parameter $s=4$. We analyze a family of exploration paths on boxes and prove tightness for this family and Holder continuity for its limiting measures. |
| title | Holder continuity of interfaces for scale-invariant Poisson stick soup |
| topic | Probability |
| url | https://arxiv.org/abs/2601.19546 |