Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2605.17494 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911692069273600 |
|---|---|
| author | Gao, Yifan Li, Ruixuan Li, Xinyi |
| author_facet | Gao, Yifan Li, Ruixuan Li, Xinyi |
| contents | We study generalized non-intersection probabilities for the three-dimensional Brownian loop soup at subcritical intensities. We establish the existence of generalized intersection exponents (GIE) and prove an up-to-constants estimate for these probabilities by means of a separation lemma tailored to this setting. We also relate the Hausdorff dimension of the set of local cut points of the three-dimensional Brownian loop soup to the GIE, and show that the GIE is continuous at intensity zero, where it reduces to the classical Brownian intersection exponent. In particular, this implies that, for sufficiently small intensity parameters, the set of local cut points has Hausdorff dimension strictly larger than $1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17494 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized intersection exponents and local cut points for three-dimensional Brownian loop soup Gao, Yifan Li, Ruixuan Li, Xinyi Probability 60J65 We study generalized non-intersection probabilities for the three-dimensional Brownian loop soup at subcritical intensities. We establish the existence of generalized intersection exponents (GIE) and prove an up-to-constants estimate for these probabilities by means of a separation lemma tailored to this setting. We also relate the Hausdorff dimension of the set of local cut points of the three-dimensional Brownian loop soup to the GIE, and show that the GIE is continuous at intensity zero, where it reduces to the classical Brownian intersection exponent. In particular, this implies that, for sufficiently small intensity parameters, the set of local cut points has Hausdorff dimension strictly larger than $1$. |
| title | Generalized intersection exponents and local cut points for three-dimensional Brownian loop soup |
| topic | Probability 60J65 |
| url | https://arxiv.org/abs/2605.17494 |