Annihilating branching processes


Journal Article

We consider Markov processes ηt ⊂ Zd in which (i) particles die at rate δ ≥ 0, (ii) births from x to a neighboring y occur at rate 1, and (iii) when a new particle lands on an occupied site the particles annihilate each other and a vacant site results. When δ = 0 product measure with density 1 2 is a stationary distribution; we show it is the limit whenever P(η0≠ ø) = 1. We also show that if δ is small there is a nontrivial stationary distribution, and that for any δ there are most two extremal translation invariant stationary distributions. © 1991.

Full Text

Duke Authors

Cited Authors

  • Bramson, M; Wan-ding, D; Durrett, R

Published Date

  • January 1, 1991

Published In

Volume / Issue

  • 37 / 1

Start / End Page

  • 1 - 17

International Standard Serial Number (ISSN)

  • 0304-4149

Digital Object Identifier (DOI)

  • 10.1016/0304-4149(91)90056-I

Citation Source

  • Scopus