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The annihilating process on random trees and the square lattice

  • Aidan Sudbury (a1)

Abstract

An annihilating process is an interacting particle system in which the only interaction is that a particle may kill a neighbouring particle. Since there is no birth and no movement, once a particle has no neighbours its site remains occupied for ever. The survival probability is calculated for a random tree and for the square lattice. A connection is made between annihilating processes and the adsorption of molecules onto surfaces. A one-dimensional adsorption problem is solved in the case in which the two neighbours do not act independently.

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Corresponding author

Postal address: School of Mathematical Sciences, Monash University, PO Box 28M, VIC 3800, Australia. Email address: aidan.sudbury@sci.monash.edu.au

References

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Arratia, R. (1981). Limiting point processes for rescaling of coalescing and annihilating random walks on ℤ d . Ann. Prob. 9, 909936.10.1214/aop/1176994264
Bramson, M., and Gray, L. (1985). The survival of the branching annihilating random walk. Z. Wahrscheinlichskeitsth. 68, 447460.10.1007/BF00535338
Bramson, M., and Griffeath, D. (1980). Asymptotics for interacting particle systems on ℤ d . Z. Wahrscheinlichskeitsth. 53, 183196.10.1007/BF01013315
Neuhauser, C., and Sudbury, A. W. (1993). The biased annihilating branching process. Adv. Appl. Prob. 25, 2438.10.2307/1427494
O'hely, M., and Sudbury, A. W. (2001). The annihilating process. J. Appl. Prob. 38, 223231.10.1239/jap/996986655
Sudbury, A. W. (2002). Inclusion-exclusion methods for treating annihilating and deposition processes. J. Appl. Prob. 39, 466478.10.1239/jap/1034082120

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The annihilating process on random trees and the square lattice

  • Aidan Sudbury (a1)

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