Stochastic models for random sets of points
J. F. C. Kingmán · 1992
Abstract Figure 1.1 might represent the positions of visible stars in a patch of the sky, the positions (seen from above) of trees in an area of woodland, or those of certain archaeological sites. There is no clear pattern, the points are haphazardly distributed with no obvious regularity or trends in density. Similar situations can arise in three dimensions or in one, or in more complicated geometries. If we look at the whole sky, for example, the stars appear to be distributed over the surface of a sphere. Poisson processes are models of such phenomena, which use the theory of probability to describe this sort of highly random behaviour. Their characteristic feature is a property of statistical independence.