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Fourier analysis of the graph of fractional Brownian motion

Tuomas Sahlsten
University of Bristol

Analysis

Organiser: Michiel van den Berg

ABSTRACT
We prove that the graph of fractional Brownian motion with any Hurst exponent is almost surely not a Salem set, that is, the Fourier dimension of the graph is strictly less than the Hausdorff dimension. This answers in part a question of J.-P. Kahane from 1993. The main tool behind our result is the slicing theory of measures, which is a classical technique in geometric measure theory. This is joint work with Jonathan Fraser (St Andrews, Scotland) and Tuomas Orponen (Helsinki, Finland).