Thick points for spatial Brownian motion: multifractal analysis of occupation measure

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Random Fractals and Markov Processes (2005, result): “We note that Dembo et al. (2000a) have obtained some partial results about ϕ-m(A).”
Thick points for planar Brownian motion and the Erdős-Taylor conjecture on random walk (2001, methodology): “Hence, as explained in [3], standard multifractal analysis must be refined in order to capture the delicate fluctuations of Brownian occupation measure and obtain a non-degenerate dimension spectrum.”