Publications [#243458] of Richard T. Durrett

Papers Published

1. Bramson, M; Wan-ding, D; Durrett, R, Annihilating branching processes, Stochastic Processes and their Applications, vol. 37 no. 1 (January, 1991), pp. 1-17, Elsevier BV, ISSN 0304-4149 [doi]
   (last updated on 2024/04/18)

   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.