2024/2025

Ergodicity and Mixing for Markov Processes

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

Where: Faculty of Mathematics

When: 3, 4 module

Open to: students of all HSE University campuses

Instructors: Cedric Bernardin

Language: English

ECTS credits: 6

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).