2024/2025

Эргодичность и перемешивание для марковских процессов

Статус: Дисциплина общефакультетского пула

Кто читает: Факультет математики

Где читается: Факультет математики

Когда читается: 3, 4 модуль

Охват аудитории: для всех кампусов НИУ ВШЭ

Преподаватели: Бернардан Седрик Жан Антуан

Язык: английский

Кредиты: 6

Контактные часы: 72

Course Syllabus

Abstract

Last decades witness fast penetrating of Probability to other fields of mathematics, first of all - to differential equations, PDEs and mathematical physics. Probability starts to enter geometry, and has rich and involved relation with the algebraic number theory. The goal of this course is to present sections of Probability, motivated by differential equations, PDEs and mathematical physics in order to justify physical thesis that "complicated systems during their evolution converge to statistical equilibria". This convergence is called "the mixing", and the thesis above is, for example, one of postulates of the theory of turbulence. (For the situation which appears there, it still is not justified due to extreme complexity of the 3d Navier-Stokes system, which governs motion of fluids and gases).