Behavior of a second class particle and its dual in Hammersley’s process
نویسندگان
چکیده
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 show that a second class particle and a dual second class particle touch with probability one, and we give some information on the area enclosed by the two trajectories, up until the first intersection point. The concept of a dual second class particle is natural within a Hammersley process, but we have not encountered it, or problems related to it, in the literature on discrete interacting particle processes.
منابع مشابه
Behavior of a second class particle in Hammersley’s process
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 t...
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