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The biased annihilating branching process

  • Claudia Neuhauser (a1) and Aidan Sudbury (a2)

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 v λ /(λ +1), the product measure with density λ/(1 +λ). It is shown that v λ /(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 v λ /(λ +1) provided the initial measure converges.

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Postal address: Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1113, USA. Partially supported by the National Science Foundation.
∗∗Postal address: Mathematics Department, Monash University, Clayton, VIC 3168, Australia.

References

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The biased annihilating branching process

  • Claudia Neuhauser (a1) and Aidan Sudbury (a2)

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