The rapid points of a complex oscillation

Details The rapid points of a complex oscillation The rapid points of a complex oscillation

2012-02-17

arxiv.org/abs/1202.3855v2

LMCS 8 (1:23) 2012

Computer Science

Computational Complexity

11 pages

Scientific paper

10.2168/LMCS-8(1:23)2012

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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