Behavior of a second class particle in Hammersley's process

Details Behavior of a second class particle in Hammersley's process Behavior of a second class particle in Hammersley's process

2006-05-08

arxiv.org/abs/math/0605199v1

EJP 2006, Vol. 11, 670-685

Mathematics

Probability

15 pages, 5 figures

Scientific paper

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.

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