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NOTE: for general audience.

Consider the system of particles on Z^d where particles are of two types, A and B, and execute simple random walks in continuous time. Particles do not interact with their own type, but when a type A particle meets a type B particle, both disappear. This system serves as a model for the chemical reaction A+B -> inert . A and B can also represent matter and antimatter. Over the late 1980s, there was a substantial amount of interest in the mathematical physics and chemical physics literature in this and related models.

Depending on the relative initial concentrations of the type A and type B particles, two basic types of behavior can occur. If there is initially more of one type than the other, then the majority type will persist, and the minority type will quickly disappear. If both types are initially present in equal concentrations, the concentrations of each will tend to 0 as time increases. The behavior in both cases is also dimension dependent, with the asymptotics being qualitatively different in low and in high dimensions. We will discuss these results and their connections with recent work on the spatial configurations of the corresponding processes.