English

The rapid points of a complex oscillation

Computational Complexity 2015-07-01 v2 Probability

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.

Keywords

Cite

@article{arxiv.1202.3855,
  title  = {The rapid points of a complex oscillation},
  author = {Paul Potgieter},
  journal= {arXiv preprint arXiv:1202.3855},
  year   = {2015}
}

Comments

11 pages

R2 v1 2026-06-21T20:20:59.989Z