Electronic Communications in Probability

Random Walks that Avoid Their Past Convex Hull

Omer Angel, Itai Benjamini, and Bálint Virág

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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.

Article information

Electron. Commun. Probab., Volume 8 (2003), paper no. 2, 6-16.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60G50: Sums of independent random variables; random walks 52A22: Random convex sets and integral geometry [See also 53C65, 60D05] 91B28

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Angel, Omer; Benjamini, Itai; Virág, Bálint. Random Walks that Avoid Their Past Convex Hull. Electron. Commun. Probab. 8 (2003), paper no. 2, 6--16. doi:10.1214/ECP.v8-1065. https://projecteuclid.org/euclid.ecp/1463608886

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