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
- Lectures 1a and 1b. Thursday 21 February:
8W2.30 (14.15 - 15.05) and 8W2.22 (16.15 - 17.05).
Lecture notes are here
- Lecture 2. Thursday 28 February:
4.15-6.00. Room 1W4.39.
Lecture notes are here
- Lecture 3. Thursday 7 March:
4.15-6.00. Room 8W2.22.
Lecture notes are here
- Lecture 4. Thursday 14 March:
4.15-6.00. Room 8W2.10
Lecture notes are here
- Lecture 5. Thursday 21 March:
4.15-6.00. Room 8W2.10
Lecture notes are here
- Lecture 6. Thursday 18 April:
4.15-6.00. Room 8W2.10
Lecture notes are here
- Lecture 7. Thursday 25 April:
4.15-6.00. Room 8W2.10
Lecture notes are here
- Lecture 8. Thursday 2 May:
4.15-6.00. Room 8W2.10
Lecture notes are here
-
This course is now finished!
Books
-
Kingman's book `Poisson Processes' is relevant to some of this
course.