On support sets of the critical Liouville Quantum Gravity
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913377900560384 |
|---|---|
| author | Biskup, Marek Gufler, Stephan Louidor, Oren |
| author_facet | Biskup, Marek Gufler, Stephan Louidor, Oren |
| contents | We study fractal properties of support sets of the critical Liouville Quantum Gravity (cLQG) associated with the Gaussian Free Field in planar domains. Specifically, we completely characterize the gauge functions $ϕ$ (subject to mild monotonicity conditions) for which the cLQG admits a support set of finite $ϕ$-Hausdorff measure. As a corollary, we settle the conjecture that the cLQG is supported on a set of vanishing Hausdorff dimension. Our proofs are based on the fact that the cLQG describes the near-critical level sets of Discrete Gaussian Free Field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02814 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On support sets of the critical Liouville Quantum Gravity Biskup, Marek Gufler, Stephan Louidor, Oren Probability Mathematical Physics 60G57, 28A78, 60G15, 60G60 We study fractal properties of support sets of the critical Liouville Quantum Gravity (cLQG) associated with the Gaussian Free Field in planar domains. Specifically, we completely characterize the gauge functions $ϕ$ (subject to mild monotonicity conditions) for which the cLQG admits a support set of finite $ϕ$-Hausdorff measure. As a corollary, we settle the conjecture that the cLQG is supported on a set of vanishing Hausdorff dimension. Our proofs are based on the fact that the cLQG describes the near-critical level sets of Discrete Gaussian Free Field. |
| title | On support sets of the critical Liouville Quantum Gravity |
| topic | Probability Mathematical Physics 60G57, 28A78, 60G15, 60G60 |
| url | https://arxiv.org/abs/2406.02814 |