Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912513186070528 |
|---|---|
| author | Chen, Yukun Lin, Zhaofeng Qiu, Yanqi |
| author_facet | Chen, Yukun Lin, Zhaofeng Qiu, Yanqi |
| contents | We determine the exact values of the Fourier dimensions for Gaussian Multiplicative Chaos measures on the $d$-dimensional torus $\mathbb{T}^d$ for all integers $d \ge 1$. This resolves a problem left open in previous works [LQT24,LQT25] for high dimensions $d\ge 3$. The proof relies on a new construction of log-correlated Gaussian fields admitting specific decompositions into smooth processes with high regularity. This construction enables a multi-resolution analysis to obtain sharp local estimates on the measure's Fourier decay. These local estimates are then integrated into a global bound using Pisier's martingale type inequality for vector-valued martingales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23494 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Chen, Yukun Lin, Zhaofeng Qiu, Yanqi Probability Mathematical Physics Functional Analysis We determine the exact values of the Fourier dimensions for Gaussian Multiplicative Chaos measures on the $d$-dimensional torus $\mathbb{T}^d$ for all integers $d \ge 1$. This resolves a problem left open in previous works [LQT24,LQT25] for high dimensions $d\ge 3$. The proof relies on a new construction of log-correlated Gaussian fields admitting specific decompositions into smooth processes with high regularity. This construction enables a multi-resolution analysis to obtain sharp local estimates on the measure's Fourier decay. These local estimates are then integrated into a global bound using Pisier's martingale type inequality for vector-valued martingales. |
| title | Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus |
| topic | Probability Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2507.23494 |