Gibbsian Point Processes
Winter semester 2022/23
This is a course for master students in Mathematics, Theoretical and Mathematical Physics, and Finance- and Insurance Mathematics. The course is egligible as Special topics in Stochastics as module WP 32 (for Math), as well as WP 43 and 44 (for TMP), resp. WP 10 (FIM, PO 2011) and WP 13 (FIM, PO 2019). Other moduls upon request.Lecturer: Dr. Matthew Dickson, Prof. Dr. Markus Heydenreich
Content:
The initial focus is on a general theory of point process with special emphasize on the Poisson process. We then introduce continuum Gibbs measures, and discuss their properties. In the sequel we focus on more specialized topics (depending on time):
- phase transitions
- cluster expansions
- spatial birth-death processes
Lecture: Mon 10-12 and Wed 10-12 in lecture hall B047
Exercise:
Weekly work sessions, Fri 14-16 in lecture hall B047
Registration: Sign up for this course via MOODLE, please (subscription key is "Gibbs").
All further communication is solely provided via moodle.
Literature:
We will loosely follow the lecture notes [Gibbsian Point Processes] by S. Jansen.
A key reference is the book [Lectures on the Poisson process] by G. Last and M. Penrose (CUP 2017).
Further references to the literature are provided during the course.
Note: During the winter semester, our group offers two courses on the master level, Stochastic Processes (SP) and Gibbsian Point Processes (GPP). Both courses are fairly independent and focus on different aspects. SP is a core module in probability theory, where many fundamental concepts are introduced, and it is therefore strongly advised to all students who plan to write a thesis in probability theory. GPP is of slightly different character, it presents a kaleidoscope of very specialized topics in a research area, and focusses in particular on the connection with (classical) statistical mechanics.