Math 595: Concentration Inequalities and Stein's Method (Fall 2019)
Goals and topics
Concentration inequalities bound the probability that a function of several random variables differs from its mean by more than a certain amount. The search for such inequalites has been a popular topic of research in the last deacades because of their importance in numeruos applications in discrete mathematics, statistical mechanics, information theory, highdimensional geometry, random matrices and others.
This course will cover several different approaches to answering the question of finding useful concentration bounds. In particular, we will study martingale method, entropy method, transportation method, isoperimetric method, Stein's method and will cover examples from current research, including dimension reduction, random matrices, Boolean analysis, spin glasses and statistical estimation. We will also look at distributional approximation techniques using Stein's method.
Logistics
Instructor  Partha Dey 

Contact  By email with subject line: "Math 595:" 
Class  TR 9:30am 10:50pm in 343 Altgeld Hall 
Office  341A Illini Hall 
Office Hrs  TBA and By appointment. I will be happy to answer your questions in my office anytime as long as I'm not otherwise engaged. 
Textbook 
There is no required textbook. Here, is a list of books which are related to our material. I will make suggestions of more resources (books and papers) throughout the semester.

Prerequisite  Some familiarity with discrete mathematics and basic probability theory is necessary. 
Grading  Grades are based on class participation; solving exercises; and scribing lecture notes and/or presenting papers or research at the end of the semester. Use this LaTeX template for scribing. 
Tentative timeline:
08/27  Overview. Moments to Tail bound. PDF (Greg Terlov) 
08/29  Concentration function and CramérChernoff bound. PDF (Kesav Krishnan) 
09/03  Sub Gamma Random variables. PDF (Amish Goel) 
09/05  JohnsonLindenstrauss Lemma & HansenWright Inequality. PDF (Qiang Wu) 
09/10  Concentration for Maximum. PDF (HsinPo Wang) 
09/12  Classical concentration inequalities. PDF (Hongqi Chen) 
09/17  McDiarmid's Inequality and its Applications. PDF (Sourya Basu) 
09/19  Gaussian Poincaré inequality. PDF (Xingyu Bai) 
09/24  Stein's method for concentration inequalities. PDF 
09/26  EfronStein and Poincaré inequalities. PDF (Siddhartha Satpathi) 
10/01  Proofs of EfronStein inequality. PDF (Felix Clemen) 
10/03  Further Applications of EfronStein inequality. PDF ( ) 
10/08  Gaussian LogSobolev inequality. PDF (Erchi Wang) 
10/10  Herbst's argument, and LSI to Poincare. PDF (Junchi Yang) 
10/15  Shannon and relative Entropy. PDF ( ) 
10/17  Subadditivy of relative entropy and LSI for Uniform {0,1}^n. PDF (HsinPo Wang) 
10/22  Application of LSI for for Uniform {0,1}^n. PDF ( ) 
10/24  Variational characterization for Entropy. PDF ( ) 
10/29  Another characterization of Entropy. PDF (Anamitra Chaudhuri) 
10/31  Concentration for Self bounding functions. PDF (Bolton Bailey ) 
11/05  Mass Transportation Principle. PDF (Aditya Deshmukh) 
11/07  Transportation cost inequality. PDF (Siddharta Satpathi ) 
11/12  Talagrand's convex distance inequality. PDF ( ) 
11/14  Transportation cost inequality for Markov Chains. PDF (Felix Clemen) 
11/19  Applications of Talagrand's convex distance inequality. PDF ( ) 
11/21  Hyper contractivity and Talagrand's L^{1}L^{2} inequality. PDF (Yifan Zhang) 
11/26  No classes. Thanksgiving break. 
11/28  
12/03  Noise operator and concentration for higher order polynomials. PDF (Xingyu Bai) 
12/05  Sharp Threshold for Boolean functions. PDF ( ) 