Note! The times of the lecture of Tue 14.3. and exercise session of Thu 16.3. are switched with each other.
Course descriptionMany complex systems in nature and society are composed of a large number of randomly interacting simple components. This course introduces you to mathematical methods for analyzing such systems, and shows how you can apply these methods to a wide range of stochastic models. The mathematical theory focuses on tightness and weak convergence of probability measures on large finite structures. Concrete examples and applications include random walks and Brownian motion, percolation and epidemics on graphs, Curie-Weiss model and Ising model, and voter model and contact process.
- 0-1 laws
- Tightness and weak convergence of probability measures
- Couplings and monotonicity
Models and examples:
- Random walk and Brownian motion
- Curie-Weiss model and Ising model
- Voter model, contact process, and totally asymmetric exclusion process
Time2016-2017 Period IV (6 weeks)
- Lectures: Mondays 10-12 in M3 and Tuesdays 12-14 in M3 (better lecture hall instead of the officially reserved M237)
- Exercises: Thursdays 14-16 in M237
Note: There has been a change in the lecture halls of the course.
PrerequisitesProbability theory (MS-E1600) and Stochastic processes (MS-C2111), or equivalent.
GradingThe course grade is determined by a score consisting of
- up to 24 points from the exam (4 problems worth 6 points each)
- up to 6 bonus points from exercises
ExamThe exam will be held on:
- Wednesday 5.4.2017 at 13:00-16:00
- Wednesday 24.5.2017 at 16:30-19:30
ExercisesThere are weekly problem sets, posted under the "Assignments" tab on this page. Written solutions to the problems are to be returned to the course homework folder (on the announcement board next to office Y249d) by Mondays at 10 am. For the grading of the course, these solutions amount to up to 6 additional points to the exam score.
In the exercise sessions on Thursdays 14-16, the course teaching assistant Alex Karrila will provide help in solving the problems. The exercise sessions may also contain brief recitations on the topics of the lectures and problems. You should think about the problems in advance, so as to be able to focus on whatever you find difficult during the time when the teaching assistant is there to help you!
Responses to feedback
Thank you to everyone who gave feedback! Below I respond to the issues that came up.
The TA and the recitations and hints in the exercise sessions got only positive comments! Encouraged by this, we will most likely keep the same general system of exercises in the future, in this course and perhaps also others.
The deadline for turning in the solutions to the exercises received some criticism. In our view, the current schedule gives almost as much time for the exercises as is possible within the 6 weeks course format. We might try to move the exercise session to earlier on during the week, in order to arrange slightly more time after receiving the hints at the expense of time to prepare before receiving the hints.
Exercises received were considered challenging, in both positive and negative comments, and one response found they repeated certain ideas. This course is indeed the most advanced regular probability course, and the exercises are supposed to correspond to that level. In the future we may in any case include more routine problems as a warm up to the challenging ones. Repetition of some key techniques has been intentional, but we will try to ensure sufficient variability as well.
Overall, the feedback was for the most part positive. We try to use it to develop the course further. Thank you for all the responses!