Abstract
We consider Markov processes η t ⊂ Z d 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(η 0≠ 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.
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