Absolute continuity of non-Gaussian and Gaussian multiplicative chaos measures
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911320749637632 |
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| author | Kim, Yujin H. Kriechbaum, Xaver |
| author_facet | Kim, Yujin H. Kriechbaum, Xaver |
| contents | In this article, we consider the multiplicative chaos measure associated to the log-correlated random Fourier series, or random wave model, with i.i.d. coefficients taken from a general class of distributions. This measure was shown to be non-degenerate when the inverse temperature is subcritical by Junnila (Int. Math. Res. Not. 2020 (2020), no. 19, 6169-6196). When the coefficients are Gaussian, this measure is an example of a Gaussian multiplicative chaos (GMC), a well-studied universal object in the study of log-correlated fields. In the case of non-Gaussian coefficients, the resulting chaos is not a GMC in general. However, we construct a coupling between the non-Gaussian multiplicative chaos measure and a GMC such that the two are almost surely mutually absolutely continuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19979 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Absolute continuity of non-Gaussian and Gaussian multiplicative chaos measures Kim, Yujin H. Kriechbaum, Xaver Probability 60G57, 60G20, 60G60, 60G15, 60G30 In this article, we consider the multiplicative chaos measure associated to the log-correlated random Fourier series, or random wave model, with i.i.d. coefficients taken from a general class of distributions. This measure was shown to be non-degenerate when the inverse temperature is subcritical by Junnila (Int. Math. Res. Not. 2020 (2020), no. 19, 6169-6196). When the coefficients are Gaussian, this measure is an example of a Gaussian multiplicative chaos (GMC), a well-studied universal object in the study of log-correlated fields. In the case of non-Gaussian coefficients, the resulting chaos is not a GMC in general. However, we construct a coupling between the non-Gaussian multiplicative chaos measure and a GMC such that the two are almost surely mutually absolutely continuous. |
| title | Absolute continuity of non-Gaussian and Gaussian multiplicative chaos measures |
| topic | Probability 60G57, 60G20, 60G60, 60G15, 60G30 |
| url | https://arxiv.org/abs/2410.19979 |