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2003 Random Walks that Avoid Their Past Convex Hull
Omer Angel, Itai Benjamini, Bálint Virág
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Electron. Commun. Probab. 8: 6-16 (2003). DOI: 10.1214/ECP.v8-1065

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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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

Information

Accepted: 16 February 2003; Published: 2003
First available in Project Euclid: 18 May 2016

zbMATH: 1009.60085
MathSciNet: MR1961285
Digital Object Identifier: 10.1214/ECP.v8-1065

Subjects:
Primary: 60K35
Secondary: 52A22 , 60G50 , 91B28

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