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.
Bibliographical noteFunding Information:
* Partially supported by NSF Grant DMS86-03437. ** This work was done while this author was visiting Cornell and supported government. *** Partially supported by the National Science Foundation, the Army Research Mathematical Sciences lnstitute at Cornell University, and a Guggenheim fellowship.