Thick points for planar Brownian motion and the Erdős-Taylor conjecture on random walk

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Thick points for spatial Brownian motion: multifractal analysis of occupation measure (2000, result): “In [6] we have obtained the corresponding results for the planar case; we emphasize that the current paper concerns only d ≥ 3.”
Late points for random walks in two dimensions (2003, methodology): “which by adapting the proof of [3], Lemma 7.”