Statistics 386: Probability in many dimensions
Winter 2013

Instructor: Professor Steve Lalley
Office: 118 Eckhart Hall
Office Hours: Wednesday 2:00 - 3:00
Phone: 702-9890
E-mail: lalley "atsign" galton.uchicago.edu

This course will cover a number of topics in probability and stochastic processes related to "high-dimensional" data. These will include

• Concentration inequalities
• Entropy and relative entropy
• Dimension reduction and projections
• Large random matrices (Wigner and Marchenko-Pastur theorems)
• An introduction to compressed sensing

Eigenvalue Distribution of a Random 1000x1000 Wigner Matrix

Bookmark this page! I will post lecture notes and other material here. Exercises (optional) are embedded in the lecture notes.

Lecture Notes:

• Concentration inequalities Current version: January 26 2013
• Gaussian Processes Current version: February 27 2013
• Random Matrices: Wigner and Marchenko-Pastur Theorems Current version:March 6 2013
• Gaussian and Wishart Ensembles: Eigenvalue Densities
• Non-Colliding Brownian Paths and the GOE Eigenvalue Density