On the Fourier dimension of fractional Brownian graphs

2025/10/10 by Lee, Cheuk Yin, Tindel, Samy
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2510.09818

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∈(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.

Citations

• Fourier dimension of the graph of fractional Brownian motion with H ≥ 1/2
• The Fourier spectrum and sumset type problems
• Hausdorff and Fourier dimension of graph of continuous additive processes

Cited by

• Fourier decay in parabolic C^1+α systems with overlaps

Related

• Fourier dimension of the graph of fractional Brownian motion with H ≥ 1/2
• Dimension of Fractional Brownian motion with variable drift
• The Fourier dimension of Brownian limsup fractals
• A Lévy area by Fourier normal ordering for multidimensional fractional Brownian motion with small Hurst index
• Sojourn time dimensions of fractional Brownian motion