Random walks that avoid their past convex hull
Probability
2011-11-10 v1
Abstract
We introduce planar random walk conditioned to avoid its past convex hull, and we show that it escapes at a positive limsup speed. Experimental results show that fluctuations from a limiting direction are on the order of n^(3/4). This behavior is also observed for the extremal investor, a natural financial model related to the planar walk.
Cite
@article{arxiv.math/0209146,
title = {Random walks that avoid their past convex hull},
author = {Omer Angel and Itai Benjamini and Balint Virag},
journal= {arXiv preprint arXiv:math/0209146},
year = {2011}
}
Comments
10 pages, 4 figures