Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 10 (2005) > Paper 12 open journal systems 


The Escape Model on a Homogeneous Tree

George Kordzakhia, University of California at Berkeley, USA


Abstract
There are two types of particles interacting on a homogeneous tree of degree d+1. The particles of the first type colonize the empty space with exponential rate 1, but cannot take over the vertices that are occupied by the second type. The particles of the second type spread with exponential rate $lambda$. They colonize the neighboring vertices that are either vacant or occupied by the representatives of the opposite type, and annihilate the particles of the type 1 as they reach them. There exists a critical value $lambda_c=(2d-1)+sqrt{(2d-1)^2-1}$ such that the first type survives with positive probability for $lambda < lambda_c$, and dies out with probability one for $lambda > lambda_c$. We also find the growth profile which characterizes the rate of growth of the type 1 in the space-time on the event of survival.


Full text: PDF

Pages: 113-124

Published on: June 9, 2005
Bibliography
  1. J.T. Cox, R. Durrett. (1981). Some limit theorems for percolation processes with necessary and sufficient conditions. Annals of Probability 9 (1981), 583--603. Math. Review 82k:60208
  2. A. Dembo, O. Zeitouni. Large Deviations Techniques and Applications. Jones and Bartlett Publishers (1993) Math. Review 95a:60034
  3. O. Häggström, R. Pemantle. First Passage Percolation and a Model for Competing Spatial Growth. Journal of Applied Probability 35 (1998), 683--692. Math. Review 2000f:60153
  4. O. Häggström, R. Pemantle. Absence of mutual unbounded growth for almost all parameter values in the two-type Richardson model. Stochastic Processes and their Applications 90 (2000), 207--222. Math. Review 2002b:60174
  5. G. Kordzakhia, S. Lalley. A two-species competition model on $mathbb{Z}^d$. Stochastic Processes and their Applications 115 (2005), 781--796. Math. Review number not available.
  6. S. Lalley. Growth profile and invariant measures for the weakly supercritical contact process on a homogeneous tree. Annals of Probability 27 (1999), 206--225. Math. Review 2000b:60239
  7. C. Neuhauser. Ergodic theorems for the multitype contact process. Probability Theory and Related Fields 91 (1992), 467--506. Math. Review 93c:60162
  8. D. Richardson, D. Random growth in tessellation. Proceedings of Cambridge Philosophical Society 74 (1973), 515--528. Math. Review 48 #7421
















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


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

Electronic Communications in Probability. ISSN: 1083-589X