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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.17219 |
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| _version_ | 1866913486638940160 |
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| author | Vihko, Sami |
| author_facet | Vihko, Sami |
| contents | We consider log-correlated random fields $X$ and the associated multiplicative chaos measures $μ_{γ,X}$. Our results reconstruct the underlying field $X$ from the multiplicative chaos measure $ν_{γ,X}$. The new feature of our results is that we allow the dimension $d$ to be arbitrary and cover also the critical case $γ=\sqrt{2d}$. In the sub-critical regime $γ<\sqrt{2d}$, we allow the fields to be mildly non-Gaussian, that is, the field has the decomposition $X=G+H$ with a log-correlated Gaussian field $G$ and a Hölder-continuos (not necessarily Gaussian) field $H$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17219 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reconstruction of log-correlated fields from multiplicative chaos measures Vihko, Sami Probability Mathematical Physics We consider log-correlated random fields $X$ and the associated multiplicative chaos measures $μ_{γ,X}$. Our results reconstruct the underlying field $X$ from the multiplicative chaos measure $ν_{γ,X}$. The new feature of our results is that we allow the dimension $d$ to be arbitrary and cover also the critical case $γ=\sqrt{2d}$. In the sub-critical regime $γ<\sqrt{2d}$, we allow the fields to be mildly non-Gaussian, that is, the field has the decomposition $X=G+H$ with a log-correlated Gaussian field $G$ and a Hölder-continuos (not necessarily Gaussian) field $H$. |
| title | Reconstruction of log-correlated fields from multiplicative chaos measures |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2408.17219 |