The Liouville model in the $L^1$ phase: coupling and extreme values
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909747784974336 |
|---|---|
| author | Hofstetter, Michael Zeitouni, Ofer |
| author_facet | Hofstetter, Michael Zeitouni, Ofer |
| contents | We establish a strong coupling between the Liouville model and the Gaussian free field on the two dimensional torus in the $L^1$ phase $β\in (0, 8π)$, such that the difference of the two fields is a Hölder continuous function. The coupling originates from a Polchinski renormalisation group approach, which was previously used to prove analogous results for other Euclidean field theories in dimension two. Our main observations for the Liouville model are that the Polchinski flow has a definite sign and can be controlled well thanks to an FKG argument.
The coupling allows to relate extreme values of the Liouville model and the Gaussian free field, and as an application we show that the global maximum of the Liouville field converges in distribution to a randomly shifted Gumbel distribtion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Liouville model in the $L^1$ phase: coupling and extreme values Hofstetter, Michael Zeitouni, Ofer Probability Mathematical Physics 60G60 We establish a strong coupling between the Liouville model and the Gaussian free field on the two dimensional torus in the $L^1$ phase $β\in (0, 8π)$, such that the difference of the two fields is a Hölder continuous function. The coupling originates from a Polchinski renormalisation group approach, which was previously used to prove analogous results for other Euclidean field theories in dimension two. Our main observations for the Liouville model are that the Polchinski flow has a definite sign and can be controlled well thanks to an FKG argument. The coupling allows to relate extreme values of the Liouville model and the Gaussian free field, and as an application we show that the global maximum of the Liouville field converges in distribution to a randomly shifted Gumbel distribtion. |
| title | The Liouville model in the $L^1$ phase: coupling and extreme values |
| topic | Probability Mathematical Physics 60G60 |
| url | https://arxiv.org/abs/2508.15689 |