Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911008627359744 |
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| author | Lin, Zhaofeng Qiu, Yanqi Tan, Mingjie |
| author_facet | Lin, Zhaofeng Qiu, Yanqi Tan, Mingjie |
| contents | We introduce a unified approach for studying the polynomial Fourier decay of classical multiplicative chaos measures. As consequences, we obtain the precise Fourier dimensions for multiplicative chaos measures arising from the following key models: the sub-critical 1D and 2D GMC (which in particular resolves the Garban-Vargas conjecture); the sub-critical $d$-dimensional GMC with $d \ge 3$ when the parameter $γ$ is near the critical value; the canonical Mandelbrot random coverings; the canonical Mandelbrot cascades. For various other models, we establish the non-trivial lower bounds of the Fourier dimensions and in various cases we conjecture that they are all optimal and provide the exact values of Fourier dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03298 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions Lin, Zhaofeng Qiu, Yanqi Tan, Mingjie Probability Mathematical Physics Dynamical Systems Functional Analysis We introduce a unified approach for studying the polynomial Fourier decay of classical multiplicative chaos measures. As consequences, we obtain the precise Fourier dimensions for multiplicative chaos measures arising from the following key models: the sub-critical 1D and 2D GMC (which in particular resolves the Garban-Vargas conjecture); the sub-critical $d$-dimensional GMC with $d \ge 3$ when the parameter $γ$ is near the critical value; the canonical Mandelbrot random coverings; the canonical Mandelbrot cascades. For various other models, we establish the non-trivial lower bounds of the Fourier dimensions and in various cases we conjecture that they are all optimal and provide the exact values of Fourier dimensions. |
| title | Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions |
| topic | Probability Mathematical Physics Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2505.03298 |