Massive SLE$_4$, massive CLE$_4$ and the massive planar GFF
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917605490556928 |
|---|---|
| author | Papon, Léonie |
| author_facet | Papon, Léonie |
| contents | We construct a coupling between a massive GFF and a random curve in which the curve can be interpreted as the level line of the field and has the law of massive SLE$_4$. This coupling is obtained by reweighting the law of the standard coupling GFF-SLE$_4$ and our result can be seen as a conditional version of the path-integral formulation of the massive GFF. We then show that by reweighting the law of the coupling GFF-CLE$_4$ in a similar way, one obtains a coupling between a massive GFF and a random countable collection of simple loops, that we call massive CLE$_4$. Using this coupling, we relate massive CLE$_4$ to the massive Brownian loop soup with intensity $1/2$, thus proving a conjecture of Camia. As the law of the massive GFF, the laws of massive SLE$_4$ and massive CLE$_4$ are conformally covariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11180 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Massive SLE$_4$, massive CLE$_4$ and the massive planar GFF Papon, Léonie Probability Mathematical Physics We construct a coupling between a massive GFF and a random curve in which the curve can be interpreted as the level line of the field and has the law of massive SLE$_4$. This coupling is obtained by reweighting the law of the standard coupling GFF-SLE$_4$ and our result can be seen as a conditional version of the path-integral formulation of the massive GFF. We then show that by reweighting the law of the coupling GFF-CLE$_4$ in a similar way, one obtains a coupling between a massive GFF and a random countable collection of simple loops, that we call massive CLE$_4$. Using this coupling, we relate massive CLE$_4$ to the massive Brownian loop soup with intensity $1/2$, thus proving a conjecture of Camia. As the law of the massive GFF, the laws of massive SLE$_4$ and massive CLE$_4$ are conformally covariant. |
| title | Massive SLE$_4$, massive CLE$_4$ and the massive planar GFF |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2312.11180 |