The rapid points of a complex oscillation

Paul Potgieter

doi:10.2168/lmcs-8(1:23)2012

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arXiv · 1202.3855

The rapid points of a complex oscillation

Paul Potgieter

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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.

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Paul Potgieter. 2012-02-17. The rapid points of a complex oscillation. https://doi.org/10.2168/lmcs-8(1:23)2012

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