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2006 Behavior of a second class particle in Hammersley's process
Eric Cator, Sergei Dobrynin
Author Affiliations +
Electron. J. Probab. 11: 670-685 (2006). DOI: 10.1214/EJP.v11-340

Abstract

In the case of a rarefaction fan in a non-stationary Hammersley process, we explicitly calculate the asymptotic behavior of the process as we move out along a ray, and the asymptotic distribution of the angle within the rarefaction fan of a second class particle and a dual second class particle. Furthermore, we consider a stationary Hammersley process and use the previous results to show that trajectories of a second class particle and a dual second class particles touch with probability one, and we give some information on the area enclosed by the two trajectories, up until the first intersection point. This is linked to the area of influence of an added Poisson point in the plane.

Citation

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Eric Cator. Sergei Dobrynin. "Behavior of a second class particle in Hammersley's process." Electron. J. Probab. 11 670 - 685, 2006. https://doi.org/10.1214/EJP.v11-340

Information

Accepted: 7 August 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1112.60076
MathSciNet: MR2242659
Digital Object Identifier: 10.1214/EJP.v11-340

Subjects:
Primary: 60C05
Secondary: 60F05, 60K35

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