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Two types of mutually annihilating particles

Published online by Cambridge University Press:  01 July 2016

Richard Holley
Richard Holley*
Affiliation:
University of Colorado, Boulder
*
∗Postal address: Department of Mathematics, University of Colorado, Campus Box 426, Boulder, CO 80309, U.S.A.
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Abstract

We consider two types of particles performing simple random walks on the integers. When two particles of different types collide they are immediately annihilated. All particles of one type are started off to the left of the origin, and all particles of the other type are started off to the right of the origin. We determine the asymptotic rate of annihilations and the fluctuations, around this rate, of the numbers annihilated at large times.

Keywords

RATE OF ANNIHILATIONRANDOM WALK
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 1 , March 1983 , pp. 133 - 148
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

∗

Research supported in part by N.S.F. Grant MCS 80–07300.

References

[1] Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
[2] Meyer, P. A. (1966) Probability and Potentials. Blaisdell, Waltham, Ma.Google Scholar
[3] Spitzer, F. (1964) Principles of Random Walk. Van Nostrand, Princeton, NJ.CrossRefGoogle Scholar