Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.
LEARNING OUTCOMES
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
Credits: 5
Schedule: 01.03.2021 - 07.04.2021
Teacher in charge (valid 01.08.2020-31.07.2022): Kalle Kytölä
Teacher in charge (applies in this implementation): Kalle Kytölä
Contact information for the course (valid 08.02.2021-21.12.2112):
Lecturer: Kalle Kytölä
Teaching assistant: Osama Abuzaid
CEFR level (applies in this implementation):
Language of instruction and studies (valid 01.08.2020-31.07.2022):
Teaching language: English
Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
Valid 01.08.2020-31.07.2022:
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
Applies in this implementation:
Theory:
- 0-1 laws
- Tightness and weak convergence of probability measures
- Couplings and monotonicity
Models and examples:
- Random walk and Brownian motion
- Percolation
- Curie-Weiss model and Ising model
- Voter model, contact process, and totally asymmetric exclusion process
Assessment Methods and Criteria
Valid 01.08.2020-31.07.2022:
Weekly exercises and exam.
Applies in this implementation:
The assessment is based on exercises and exam, but the details in remote mode are yet to be fixed.
Workload
Valid 01.08.2020-31.07.2022:
- 2 x 2h lectures
- 1 x 2h exercises sessions
DETAILS
Study Material
Valid 01.08.2020-31.07.2022:
Kemppainen and Kytölä: Large Random Systems, lecture notes, 2019.
Applies in this implementation:
Prerequisites
Valid 01.08.2020-31.07.2022:
MS-E1600 Probability Theory
- Teacher: Abuzaid Osama
- Teacher: Kytölä Kalle