High-dimensional probability

Department: 
Math
Course Number: 
7251
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every Spring starting Sp 2021

The goal of this PhD level graduate course is to provide a rigorous introduction to the methods of high-dimensional probability.

Prerequisites: 

MATH 6241

Course Text: 

At the level of R. Vershynin, High-Dimensional Probability. An Introduction with Applications in Data Science, Cambridge University Press, 2018.

Topic Outline: 

- Concentration inequalities : Bernstein-type, the Hanson-Wright inequality, Talagrand's inequality for product measures, concentration on the Gaussian measure space.

 - Gaussian processes: Slepian's, Sudakov's inequalities; Dudley's and Talagrand's chaining.

 - Non-asymptotic random matrix theory: the condition number of Gaussian matrices, elements of the Littlewood-Offord theory, compressed sensing and the Restricted Isometry Property, applications of the resolvent method and the trace method.