ar X iv : m at h / 06 03 34 5 v 1 [ m at h . PR ] 1 4 M ar 2 00 6 Second class particles and cube root asymptotics for Hammersley ’ s process
نویسندگان
چکیده
We show that, for a stationary version of Hammersley's process, with Poisson sources on the positive x-axis and Poisson sinks on the positive y-axis, the variance of the length of a longest weakly NorthEast path L(t, t) from (0, 0) to (t, t) is equal to 2E(t − X(t)) + , where X(t) is the location of a second class particle at time t. This implies that both E(t − X(t)) + and the variance of L(t, t) are of order t 2/3. Proofs are based on the relation between the flux and the path of a second class particle, continuing the approach of Cator and Groeneboom (2005).
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