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arXiv · 2510.09818

On the Fourier dimension of fractional Brownian graphs

Cheuk Yin Lee·Samy Tindel
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Abstract

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.

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Cheuk Yin Lee, Samy Tindel. 2025-10-10. On the Fourier dimension of fractional Brownian graphs. https://arxiv.org/abs/2510.09818

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