On the Fourier dimension of fractional Brownian graphs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911203707584512 |
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| author | Lee, Cheuk Yin Tindel, Samy |
| author_facet | Lee, Cheuk Yin Tindel, Samy |
| contents | In this note we prove that the Fourier dimension of the graph $G(B)$ of a fractional Brownian motion $B$ with Hurst parameter $H\in(0,1/2)$ is equal to 1. This finishes to solve a conjecture by Fraser and Sahlsten. It also yields an exact formula for the gap $\dim_{\rm H}(G(B)) - \dim_{\rm F}(G(B))$ between the Hausdorff dimension and the Fourier dimension of $G(B)$. The proof is based on an intricate combinatorics procedure for multiple integrals related to the covariance function of the fractional Brownian motion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09818 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Fourier dimension of fractional Brownian graphs Lee, Cheuk Yin Tindel, Samy Probability In this note we prove that the Fourier dimension of the graph $G(B)$ of a fractional Brownian motion $B$ with Hurst parameter $H\in(0,1/2)$ is equal to 1. This finishes to solve a conjecture by Fraser and Sahlsten. It also yields an exact formula for the gap $\dim_{\rm H}(G(B)) - \dim_{\rm F}(G(B))$ between the Hausdorff dimension and the Fourier dimension of $G(B)$. The proof is based on an intricate combinatorics procedure for multiple integrals related to the covariance function of the fractional Brownian motion. |
| title | On the Fourier dimension of fractional Brownian graphs |
| topic | Probability |
| url | https://arxiv.org/abs/2510.09818 |