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.
Citation
Omer Angel. Itai Benjamini. Bálint Virág. "Random Walks that Avoid Their Past Convex Hull." Electron. Commun. Probab. 8 6 - 16, 2003. https://doi.org/10.1214/ECP.v8-1065
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