Магистратура
2024/2025
Научно-исследовательский семинар "Представления и вероятность 1"
Статус:
Курс по выбору (Математика)
Направление:
01.04.01. Математика
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
1-й курс, 1, 2 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для всех кампусов НИУ ВШЭ
Прогр. обучения:
Математика
Язык:
английский
Кредиты:
3
Course Syllabus
Abstract
The seminar is mostly aimed to 3-4th year bachelor students, as well as master and PhD students. Senior participants are expected to deliver a talk on the seminar. The seminar topics are the mix of modern results in areas related to representations and probability theory, and older areas, which are prerequisites to the former, as well as keep their own value.
Learning Objectives
- The seminar is intended to introduce the subject area to the students, and to offer them an opportunity to prepare and give a talk.
Expected Learning Outcomes
- Successful participants imporve their presentation skills and prepare for participation in research projects in the subject area.
Course Contents
- Continuous-time Markov chains and their asymptotical behavior.
- Empirical and invariant measures for Markov chains. Potential theory for Markov chains
- Determinantal point processes. Results connecting them with Markov chains.
- Large-time behavior of diffusion process. Applications to non-equilibrium statistical mechanics.
Interim Assessment
- 2024/2025 2nd moduleParticipants can make a talk during the semester (this is usually graded with a mark 6-8) and/or solve the problems of the final exam. The problems list is given to the students approximately a week before the exam, and on the exam a student discusses the solutions that he/she obtained. Formula for calculating the final grade for the exam is provided along with the problems list.
Bibliography
Recommended Core Bibliography
- Kuksin, S. B., & Shirikyan, A. (2012). Mathematics of Two-Dimensional Turbulence. Cambridge, [England]: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=480318
Recommended Additional Bibliography
- Meyn, S. P., & Tweedie, R. L. (2009). Markov Chains and Stochastic Stability (Vol. 2nd ed). Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=313161