An Informal Guide to the Theory of Conditioning in Point Processes

Abstract

Summary This paper is intended as an informal introduction to some basic results about conditioning in point processes, where we emphasize the historical background, physical motivation and intuitive understanding. The basic object of study is the conditional distribution of a point process g in a region B, given the configuration in the complement B'. As B' shrinks to the finite subsets of g, we obtain in the limit the so called Palm measures. If instead we let B shrink to individual points, we get the Papangelou conditional intensity measure. For intermediate cases, the natural description is in terms of the Gibbs and Papangelou kernels. The general theory links these concepts together in various ways.