Uniqueness of supercritical Gaussian multiplicative chaos
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909929623781376 |
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| author | Bertacco, Federico Hairer, Martin |
| author_facet | Bertacco, Federico Hairer, Martin |
| contents | We show that, for general convolution approximations to a large class of log-correlated Gaussian fields, the properly normalised supercritical Gaussian multiplicative chaos measures converge stably to a nontrivial limit. This limit depends on the choice of regularisation only through a multiplicative constant and can be characterised as an integrated atomic measure with a random intensity expressed in terms of the critical Gaussian multiplicative chaos. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07552 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniqueness of supercritical Gaussian multiplicative chaos Bertacco, Federico Hairer, Martin Probability Mathematical Physics We show that, for general convolution approximations to a large class of log-correlated Gaussian fields, the properly normalised supercritical Gaussian multiplicative chaos measures converge stably to a nontrivial limit. This limit depends on the choice of regularisation only through a multiplicative constant and can be characterised as an integrated atomic measure with a random intensity expressed in terms of the critical Gaussian multiplicative chaos. |
| title | Uniqueness of supercritical Gaussian multiplicative chaos |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2504.07552 |