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Diffusion-reaction in one dimension

Published online by Cambridge University Press:  14 July 2016

David Balding
David Balding*
Affiliation:
University of Oxford
*
∗Postal address: Trinity College, Oxford, OX1 3BH, UK.
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Abstract

One-dimensional, periodic and annihilating systems of Brownian motions and random walks are defined and interpreted in terms of sizeless particles which vanish on contact. The generating function and moments of the number pairs of particles which have vanished, given an arbitrary initial arrangement, are derived in terms of known two-particle survival probabilities. Three important special cases are considered: Brownian motion with the particles initially (i) uniformly distributed and (ii) equally spaced on a circle and (iii) random walk on a lattice with initially each site occupied. Results are also given for the infinite annihilating particle systems obtained in the limit as the number of particles and the size of the circle or lattice increase. Application of the results to the theory of diffusion-limited reactions is discussed.

Keywords

ANNIHILATING BROWNIAN MOTIONANNIHILATING RANDOM WALKINTERACTING PARTICLE SYSTEMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 4 , December 1988 , pp. 733 - 743
Copyright
Copyright © Applied Probability Trust 1988 

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