2021/2022

Научно-исследовательский семинар "Представления и вероятность 1"

Статус: Дисциплина общефакультетского пула

Кто читает: Факультет математики

Где читается: Факультет математики

Когда читается: 1, 2 модуль

Охват аудитории: для всех кампусов НИУ ВШЭ

Преподаватели: Дымов Андрей Викторович, Клименко Алексей Владимирович, Мариани Мауро, Ольшанский Григорий Иосифович

Язык: английский

Кредиты: 3

Контактные часы: 30

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.

Assessment Elements

• Talk
• Exam

Interim Assessment

• 2021/2022 2nd module
  The final grade is the maximum of the two grades: the grade for the talk (if the student gave it) and the exam grade.

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