The course is aimed at second-year and third-year mathematics students who have completed an introductory course on probability theory. The goal of the course is to describe a number of topics from modern probability theory that are centred around random walks. Random walks are key examples of random processes, and have been used to model a variety of different phenomena in physics, chemistry, biology and beyond. The plan of the course is to introduce the basic theory of random walks (e.g. recurrence properties, limit theorems) as well as some selected related theoretical and applied topics, including: electrical networks, random polymers, financial derivatives and Black-Scholes formula.

**Material**

The course material is based on lecture notes (available online) written by Markus Heydenreich, Frank den Hollander, Evgeny Verbitskiy.

**College hours**

2 per week

Beside the lecture hours, there will be a weekly question-hour to discuss exercises which will be assigned during the lectures.

**Examination**

Written exam

**Lecture notes**

1) M. Heydenreich, F. den Hollander, E. Verbitskiy. Random Walks

http://websites.math.leidenuniv.nl/probability/