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The rapid points of a complex oscillation (1202.3855v2)
Published 17 Feb 2012 in cs.CC and math.PR
Abstract: By considering a counting-type argument on Brownian sample paths, we prove a result similar to that of Orey and Taylor on the exact Hausdorff dimension of the rapid points of Brownian motion. Because of the nature of the proof we can then apply the concepts to so-called complex oscillations (or 'algorithmically random Brownian motion'), showing that their rapid points have the same dimension.