Growth-fragmentations, Brownian cone excursions and SLE(6) explorations of a quantum disc
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912178303401984 |
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| author | Da Silva, William Powell, Ellen Watson, Alexander |
| author_facet | Da Silva, William Powell, Ellen Watson, Alexander |
| contents | The aim of this article is to present a growth-fragmentation process naturally embedded in a Brownian excursion from boundary to apex in a cone of angle $2π/3$. This growth-fragmentation process corresponds, via the so-called mating-of-trees encoding arXiv:1409.7055, to the quantum boundary length process associated with a branching $\mathrm{SLE}_6$ exploration of a $γ= \sqrt{8/3}$ quantum disc. However, our proof uses only Brownian motion techniques, and along the way we discover various properties of Brownian cone excursions and their connections with stable Lévy processes. Assuming the mating of trees encoding, our results imply several fundamental properties of the $γ= \sqrt{8/3}$-quantum disc $\mathrm{SLE}_6$-exploration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03010 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Growth-fragmentations, Brownian cone excursions and SLE(6) explorations of a quantum disc Da Silva, William Powell, Ellen Watson, Alexander Probability Mathematical Physics The aim of this article is to present a growth-fragmentation process naturally embedded in a Brownian excursion from boundary to apex in a cone of angle $2π/3$. This growth-fragmentation process corresponds, via the so-called mating-of-trees encoding arXiv:1409.7055, to the quantum boundary length process associated with a branching $\mathrm{SLE}_6$ exploration of a $γ= \sqrt{8/3}$ quantum disc. However, our proof uses only Brownian motion techniques, and along the way we discover various properties of Brownian cone excursions and their connections with stable Lévy processes. Assuming the mating of trees encoding, our results imply several fundamental properties of the $γ= \sqrt{8/3}$-quantum disc $\mathrm{SLE}_6$-exploration. |
| title | Growth-fragmentations, Brownian cone excursions and SLE(6) explorations of a quantum disc |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2501.03010 |