## UU local course:

# Master Seminar Stochastics (WISM563)

## Course description:

The master seminar stochastics will introduce students to topics at the current forefront of research in probability theory and statistical physics.

The focus of the course are stochastic models that describe various phenomena in the real world, such as magnetization, interactions between gas particles, the flow of a liquid through a porous medium and the spread of epidemics, while at the same time possessing the mathematical beauty and sophistication that makes them exciting objects of study in their own right.

In recent years, there has been significant progress in the area of the course, of considerable mathematical depth (as evidenced for instance by several recent fields medals for results in this area).

In the academic year 2016-2017, we will cover a selection of topics that will include:

- random and self-avoiding walks
- (critical) percolation, Schramm-Loewner evolution
- the contact process
- the Gibbs model
- the Ising model
- the voter model

## Literature

- Geoffrey Grimmett, "Probability on Graphs: Random processes on Graphs and Lattices", Cambridge University Press 2010, ISBN 978-0-521-14735-4
- Selected research articles to be determined during the course.

## Time and location

The course takes place in semester I (blok 1 and 2) of 2016-2017.

Meetings take place on Mondays, 13.15-15.00 in room BBL075.
**NOTA BENE:** the first meeting takes place on 19 September.

## Responsible staff member

## Course format

In the academic year 2016-2017, we will mostly follow the book by Grimmett "Probability on Graphs: Random processes on Graphs and Lattices". Each week, one of the participants will give a lecture (2x45 min) presenting part of the material, and he/she will prepare a handout that includes a homework problem for the others. (To be handed in the at the next meeting, and graded by the person giving the lecture)

## Prerequisites

The course requires a basic knowledge of probability theory and measure theory. On the other hand, it requires significant mathematical maturity.

## Evaluation

Lecture, quality of the handout and grades for the exercises.

The course is worth 7.5 ects.

## Practical matters

This seminar is aimed at master students and advanced bachelor students. Other interested participants can volunteer to give a talk, depending on availability. There is a maximal number of (active) participants to the seminar of 10, with priority given to the designated students.

All communication in the course (including the student lectures) will be in English.
The week before your presentation you should make an appointment with the responsible staff member to discuss your plan for the lecture (what you will skip etc.). This is your responsibility.
** Attendance of all meetings is mandatory. **

## Weekly schedule

- 26 Sept : Ch. 1 (Jurriaan).
- 3 Oct : Ch. 2 (Sophie).
- 10 Oct : Ch. 3 (Folkert).
- 17 Oct : Ch.5.1 and 5.3 (Lucas).
- 24 Oct : Ch. 5.5 and 5.6 (Niels).
- 31 Oct : Ch. 5.4 and 5.7 (Marieke).
- 14 Nov : Ch. 6 (Luminita).
- 21 Nov : Ch. 7 (Stefan).
- More meetings yet to be scheduled!