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Random walks

Vak
2022-2023

Admission requirements

Description

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.

Course objectives

Timetable

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

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different

Mode of instruction

Assessment method

Homework (30%) and written exam (70%)

Reading list

1) M. Heydenreich, F. den Hollander, E. Verbitskiy. Random Walks http://websites.math.leidenuniv.nl/probability/

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

Registration

From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.
Extensive FAQ's on MyStudymap can be found here.

Contact

Remarks

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