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The size of the region occupied by one type in an invasion process

Published online by Cambridge University Press:  14 July 2016

Aidan Sudbury
Aidan Sudbury*
Affiliation:
Monash University, Melbourne, Australia
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Abstract

Particles are situated on a rectangular lattice and proceed to invade each other's territory. When they are equally competitive this creates larger and larger blocks of one type as time goes by. It is shown that the expected size of such blocks is equal to the expected range of a simple random walk.

Keywords

SPATIAL PROCESSESCOMPETITION OF SPECIESDISCRETE DIFFUSONINVASION
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976 , pp. 355 - 356
Copyright
Copyright © Applied Probability Trust 1976 

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References

Clifford, P. and Sudbury, A. W. (1973) A model for spatial conflict. Biometrika 60, 581–588.CrossRefGoogle Scholar
Dvoretzky, A. and Erdös, P. (1951) Some problems on random walk in space. Proc. 2nd Berkeley Symp. Math. Statist. Prob. , 353–367.Google Scholar