Random walks that avoid their past convex hull

Omer Angel; Itai Benjamini; Balint Virag

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Random walks that avoid their past convex hull

Omer Angel·Itai Benjamini·Balint Virag

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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.

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Omer Angel, Itai Benjamini, Balint Virag. 2002-09-12. Random walks that avoid their past convex hull. https://arxiv.org/abs/math/0209146

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