The biased annihilating branching process
- 1 March 1993
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 25 (1) , 24-38
- https://doi.org/10.2307/1427494
Abstract
In the biased annihilating branching process, particles place offspring on empty neighboring sites at rate A and destroy neighbors at rate 1. It is conjectured that for any λ ≥ 0 the population will spread to ∞, and this is shown in one dimension for The process on a finite graph when starting with a non-empty configuration has limiting distribution vλ /(λ +1), the product measure with density λ/(1 +λ). It is shown that vλ /(λ +1) and δ Ø are the only stationary distributions on Moreover, if and the initial configuration is non-empty, then the limiting measure is vλ /(λ +1) provided the initial measure converges.Keywords
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