Credits: 5

Schedule: 25.02.2019 - 10.04.2019

Contact information for the course (applies in this implementation): 

Lecturer: Kalle Kytölä (firstname dot lastname at aalto dot fi)

Teaching assistant (TA): Joona Karjalainen (firstname dot lastname at aalto dot fi)

Teaching Period (valid 01.08.2018-31.07.2020): 

IV Spring (2018-2019)

Not lectured (2019-2020)

Lectured every other year


Learning Outcomes (valid 01.08.2018-31.07.2020): 

After completing the course the participant is able to:

- Formulate mathematical models of various systems with a large number of interacting random components

- Incorporate spacial structure and dynamics into probabilistic models

- Estimate the asymptotics of probabilities and expected values in models with a size parameter

- Formulate qualitative phase transitions in stochastic models and recognize them

- Verify if a sequence of probability distributions on a metric space converges


Content (valid 01.08.2018-31.07.2020): 

 Stochastic models with spatial and temporal structure

- 0-1 laws

- Large deviation estimates of rare events

- Phase transitions in stochastic models

- Convergence and tightness of probability measures


Assessment Methods and Criteria (valid 01.08.2018-31.07.2020): 

Weekly exercises and exam.

Elaboration of the evaluation criteria and methods, and acquainting students with the evaluation (applies in this implementation): 

The grade is based on exam score plus bonus points from weekly exercises.

Exam: 0-24 points

Exercises: 0-6 bonus points added to the exam score

Workload (valid 01.08.2018-31.07.2020): 

- 2 x 2h lectures

- 1 x 2h exercises sessions


Study Material (valid 01.08.2018-31.07.2020): 

Kemppainen and Kytölä: Large Random Systems, lecture notes, 2017.


Details on the course materials (applies in this implementation): 

Kemppainen & Kytölä: Large Random Systems, lecture notes

Substitutes for Courses (valid 01.08.2018-31.07.2020): 



Course Homepage (valid 01.08.2018-31.07.2020):

Prerequisites (valid 01.08.2018-31.07.2020): 



Grading Scale (valid 01.08.2018-31.07.2020): 



Registration and further information