Quantum Operators in Classical Probability Theory: II. The Concept of Duality in Interacting Particle Systems

Abstract

Duality has proved to be a powerful tool in the theory of interacting particle systems. The approach in this paper is algebraic rather than via Harris diagrams. A form of duality is found which includes coalescing and annihilating duality as special cases. This enables new results for the branching annihilating random walk and the biased annihilating branching process to be derived.