Some Annihilating Particle Systems.

Available from UMI in association with The British Library. Requires signed TDF. Systems of annihilating and coalescing particles on both infinite and periodic one-dimensional state spaces are studied. These systems have various applications in the physical sciences, in particular they are useful as simple models of diffusion-limited reactions. A unified approach to computing properties of the systems using duality methods is presented and it is shown that many results in the scientific literature, derived using diverse techniques, are readily obtained in this general framework. The transition distributions of the processes with arbitrary initial configurations are characterized in terms of two-particle annihilation processes. Further, a concise expression for the distribution of the cardinality of the processes with finite initial configurations is given and particular cases of interest from the applications perspective are described in detail. Asymptotic site occupancies, previously known for certain classes of initial configurations, are derived for all spatially stationary configurations. The asymptotic spatial structure is described for many cases by showing convergence to point processes whose properties are given.