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):
https://mycourses.aalto.fi/course/search.php?search=MS-E1602
Prerequisites (valid 01.08.2018-31.07.2020):
MS-E1600
Grading Scale (valid 01.08.2018-31.07.2020):
0-5
- Teacher: Kytölä Kalle