Poisson processes and Stochastic Geometry

Graduate course, Semester II 2012-13

The Poisson process, along with Brownian motion, is one of the most fundamental constructions in Probability. Traditionally, by comparison with Brownian motion the `humble Poisson process' has often been neglected as object of study. In fact there is an interesting theory of stochastic analysis of the Poisson process over abstract spaces. The Poisson process is particularly important in models of stochastic geometry, some of which we shall discuss.

Provisional list of topics

We aim to discuss many of the following (there probably won't be time to cover them all). Basics: point and Poisson processes; characteristic functional; construction; moment formulae; mappings, markings and thinnings. Related models in stochastic geometry; Cox processes, continuum percolation, poisson cluster processes, Permanental point processes. Stochastic analysis over Poisson spaces; Margulis-Russo formula, Fock space represenation, covariance identities, chaos expansion.

Lecture schedule/Diary

Books