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July 2000 The survival of nonattractive interacting particle systems on Z
Aidan Sudbury
Ann. Probab. 28(3): 1149-1161 (July 2000). DOI: 10.1214/aop/1019160329


We consider interacting particle systems on $Z$ which allow five types of pairwise interaction: Annihilation, Birth, Coalescence, Death and Exclusion with corresponding rates a, b,c, d, e . We show that whatever the values of a, c, d, e, if the birthrate is high enough there is a positive probability the particle system will survive starting from any finite occupied set. In particular: an IPS with rates a b c d e has a positive probability of survival if

$$ b > 4d + 6a, \quad c + a \geq d + e$$


$$ b > 7d + 3a - 3c + 3e, \quad c + a < d + e.$$

We create a suitable supermartingale by extending the method used by Holley and Liggett in their treatment of the contact process.


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Aidan Sudbury. "The survival of nonattractive interacting particle systems on Z." Ann. Probab. 28 (3) 1149 - 1161, July 2000.


Published: July 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1023.60087
MathSciNet: MR1797307
Digital Object Identifier: 10.1214/aop/1019160329

Primary: 60K35

Keywords: contact process , critical values , interacting particle systems , submartingale

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 3 • July 2000
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