Math @ Duke

Publications [#243458] of Richard T. Durrett
Papers Published
 Bramson, M; Wanding, D; Durrett, R, Annihilating branching processes,
Stochastic Processes and their Applications, vol. 37 no. 1
(1991),
pp. 117, ISSN 03044149
(last updated on 2017/12/16)
Abstract: 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.


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