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The survival of various interacting particle systems

  • Aidan Sudbury (a1)

Abstract

Particles may be removed from a lattice by murder, coalescence, mutual annihilation and simple death. If the particle system is not to die out, the removed particles must be replaced by births. This letter shows that coalescence can be counteracted by arbitrarily small birth-rates and contrasts this with the situations for annihilation and pure death where there are critical phenomena. The problem is unresolved for murder.

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Copyright

Corresponding author

* Postal address: Department of Mathematics, Monash University, Clayton, VIC 3168, Australia.

References

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Arratia, R. (1981) Limiting point processes for rescaling of coalescing and annihilating random walks on. Ann. Prob. 9, 909936.
Bramson, M. and Gray, L. (1985) The survival of the branching annihilating random walk. Z. Wahrscheinlichkeitsth. 68, 447460.
Bramson, M. and Griffeath, D. (1980) Asymptotics for interacting particle systems on d. Z. Wahrscheinlichkeitsth. 53, 183196.
Clifford, P. and Sudbury, A. (1979) On the use of bounds in the statistical analysis of spatial processes. Biometrika 66, 495504.
Durrett, R. (1988) Lecture Notes on Particle Systems and Percolation. Wadsworth and Brooks, Pacific Grove, California.
Harris, T. E. (1974) Contact interactions on a lattice. Ann. Prob. 2, 969988.
Holley, R. and Liggett, T. M. (1978) The survival of contact processes. Ann. Prob. 6, 198206.
Mountford, T. (1993) A coupling of finite particle systems. J. Appl. Prob. 30, 258262.
Neuhauser, C. and Sudbury, A. (1993) The biased annihilating branching process. Adv. Appl. Prob. 25, 2438.

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The survival of various interacting particle systems

  • Aidan Sudbury (a1)

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