PROPERTIES OF COMPOUND POISSON PROCESSES WITH APPLICATIONS IN STATISTICAL PHYSICS

The concept of a compound Poisson process, which has on occasion been successfully applied in the analysis of statistical behaviour in social and biological systems, is shown to be a useful one for the treatment of certain types of random process in physics. Some properties of this class of statistical distribution are derived and illustrated by various applications including the theory of electron avalanche development and the non-steady state distribution of radiation in a cavity. If the elements of a given process form a homogeneous ensemble, then the question of whether the process is or is not a compound Poisson process is decided in general by whether the correlations in the number of elements are positive or negative. It is pointed out that an analogous distinction may be drawn between the two forms of quantum statistics. © 1969.