Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866908350981079040 |
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| author | Lin, Zhaofeng Qiu, Yanqi Tan, Mingjie |
| author_facet | Lin, Zhaofeng Qiu, Yanqi Tan, Mingjie |
| contents | In this paper, we establish the exact Fourier dimensions of all standard sub-critical Gaussian multiplicative chaos on the unit interval, thereby confirming the Garban-Vargas conjecture. The proof relies on a significant improvement of the vector-valued martingale method, initially developed by Chen-Han-Qiu-Wang in the studies of the Fourier dimensions of Mandelbrot cascade random measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC Lin, Zhaofeng Qiu, Yanqi Tan, Mingjie Probability Mathematical Physics Dynamical Systems Functional Analysis In this paper, we establish the exact Fourier dimensions of all standard sub-critical Gaussian multiplicative chaos on the unit interval, thereby confirming the Garban-Vargas conjecture. The proof relies on a significant improvement of the vector-valued martingale method, initially developed by Chen-Han-Qiu-Wang in the studies of the Fourier dimensions of Mandelbrot cascade random measures. |
| title | Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC |
| topic | Probability Mathematical Physics Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2411.13923 |