Second class particles and cube root asymptotics for Hammersley's process
| dc.creator | Cator, Eric | |
| dc.creator | Groeneboom, Piet | |
| dc.date | 2006-03-14 | |
| dc.date | 2006-09-21 | |
| dc.date.accessioned | 2026-07-07T07:06:53Z | |
| dc.date.available | 2026-07-07T07:06:53Z | |
| dc.description | 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 North--East path $L(t,t)$ from $(0,0)$ to $(t,t)$ is equal to $2\mathbb {E}(t-X(t))_+$, where $X(t)$ is the location of a second class particle at time $t$. This implies that both $\mathbb {E}(t-X(t))_+$ 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 [Ann. Probab. 33 (2005) 879--903]. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117906000000089 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0603345 | |
| dc.identifier | http://arxiv.org/abs/math/0603345 | |
| dc.identifier | Annals of Probability 2006, Vol. 34, No. 4, 1273-1295 | |
| dc.identifier | doi:10.1214/009117906000000089 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110190 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60C05, 60K35 (Primary) 60F05 (Secondary) | |
| dc.title | Second class particles and cube root asymptotics for Hammersley's process | |
| dc.type | text |