Random Walks that Avoid Their Past Convex Hull
Omer Angel, Weizmann Institute of Science
Itai Benjamini, Weizmann Institute of Science
Bálint Virág, MIT
Abstract
We explore planar random walk conditioned to avoid its past convex hull. We
prove that it escapes at a positive lim sup 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.
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