UBC Mathematics Department
Abstract: If a mathematical or physical object can be thought of as being built up from components of various sizes then one can consider, for a randomly chosen object, the distribution of the components ranked by size. This leads to probability distributions on the set of infinite sequences (x, y, z, ... ) such that x >= y >= z >= ... >= 0 and x + y + z + ... = 1.
An interesting family of such distributions, the Poisson-Dirichlet distributions, pops up frequently in seemingly diverse parts of pure and applied mathematics. By examining features common to several examples, one is lead to characterizations of the Poisson-Dirichlet family which were found recently by Pitman and by Zabell.