Home | Contents | Submissions, editors, etc. | Login | Search | ECP
 Electronic Journal of Probability > Vol. 11 (2006) > Paper 26 open journal systems 


Behavior of a second class particle in Hammersley's process

Eric Cator, Delft University of Technology
Sergei Dobrynin, Delft University of Technology


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.


Full text: PDF

Pages: 670-685

Published on: August 7, 2006
Bibliography
  1. Aldous, D.; Diaconis, P. Hammersley's interacting particle process and longest increasing Probab. Theory Related Fields 103 (1995), no. 2, 199--213. MR1355056 (96k:60017)
  2. Cator, Eric; Groeneboom, Piet. Hammersley's process with sources and sinks. Ann. Probab. 33 (2005), no. 3, 879--903. MR2135307 (2006b:60216)
  3. bibitem[Colleti and Pimentel (2006)]{ColPim} {small sc Colleti C. and Pimentel, L.P.R.} (2006). {em Beta-paths in the Hammersley process.} (arXiv:math.PR/0603382)
  4. Ferrari, P. A.; Kipnis, C. Second class particles in the rarefaction fan. Ann. Inst. H. Poincaré Probab. Statist. 31 (1995), no. 1, 143--154. MR1340034 (96m:60236)
  5. Groeneboom, Piet. Hydrodynamical methods for analyzing longest increasing J. Comput. Appl. Math. 142 (2002), no. 1, 83--105. MR1910520 (2003f:60022)
  6. Hammersley, J. M. A few seedlings of research. pp. 345--394. Univ. California Press, Berkeley, Calif., 1972. MR0405665 (53 #9457)
  7. Liggett, Thomas M. Stochastic interacting systems: contact, voter and exclusion of Mathematical Sciences], 324. Springer-Verlag, Berlin, 1999. xii+332 pp. ISBN: 3-540-65995-1 MR1717346 (2001g:60247)
  8. Seppäläinen, Timo. Diffusive fluctuations for one-dimensional totally asymmetric Comm. Math. Phys. 229 (2002), no. 1, 141--182. MR1917677 (2003g:82069)
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | ECP

Electronic Journal of Probability. ISSN: 1083-6489