Abstract
We study a model on the non-negative half line ℤ,+0, {0, 1, 2, . . .} in which particles created at the origin at rate 1 jump to the right at rate 1. If a particle jumps onto an already occupied site the two particles annihilate each other. In addition, whenever a particle jumps its closest neighbor to the right jumps along with it. We find that the spatial decay rate of the particle density in the stationary state is of order 1/√x at distance x from the origin. This model provides an approximation to the dynamics of an anchored Toom interface which can be represented as a spin-exchange model.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 187-208 |
| Number of pages | 22 |
| Journal | Stochastic Processes and their Applications |
| Volume | 64 |
| Issue number | 2 |
| DOIs | |
| State | Published - Nov 29 1996 |
Bibliographical note
Funding Information:* Corresponding author. ’ Supported in part by the National Science Foundation under grant DMR-92-13424. 2 Supported in part by the National Science Foundation under grant DMS-94-03644. Alfred P. Sloan Research Fellow.
Funding Information:
The authors wish to thank Maury Bramson and E. Speer for fruitful discussions in the beginning of the project. The second author wishes to acknowledge support from the Institute for Mathematics and its Applications during the winter and spring quarter 1994. The third author wishes to acknowledge support from the Courant Institute, New York, the Universita di Roma Tor vergata, and SPIC Science Foundation Madras.
Keywords
- Annihilating random walk
- Coalescing random walk
- Interacting particle systems
- Interface problems
- Toom model
- Voter model