A coupling for the Liouville and the sinh-Gordon model in the $L^2$ phase
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918169903366144 |
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| author | Hofstetter, Michael |
| author_facet | Hofstetter, Michael |
| contents | Using a stochastic control approach we establish couplings of the Liouville field and the sinh-Gordon field with the Gaussian free field in dimension $d=2$, such that the difference is in a Sobolev space of regularity $α>1$. The analysis covers the entire $L^2$ phase. Our main tools are estimates for the short scales of the minimiser of the variational problem and several applications of the Brascamp-Lieb inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21563 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A coupling for the Liouville and the sinh-Gordon model in the $L^2$ phase Hofstetter, Michael Probability Mathematical Physics Using a stochastic control approach we establish couplings of the Liouville field and the sinh-Gordon field with the Gaussian free field in dimension $d=2$, such that the difference is in a Sobolev space of regularity $α>1$. The analysis covers the entire $L^2$ phase. Our main tools are estimates for the short scales of the minimiser of the variational problem and several applications of the Brascamp-Lieb inequality. |
| title | A coupling for the Liouville and the sinh-Gordon model in the $L^2$ phase |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2510.21563 |