Topics in High-Dimensional Probability

This course covers a selection of topics in high-dimensional probability, the study of random objects, such as vectors or matrices, that take value in a high-dimensional space. We will cover classical concentration inequalities, such as Hoeffding and Chernoff inequalities, functional inequalities, such as the Poincare and log-Sobolev inequalities, as well as subgaussian and subexponential distributions. Students will have the opportunity to learn about further topics in high-dimensional probability by preparing a presentation on a topic of their choice as well as writing a report on the same topic; opportunities for instructor guidance will be given. Prerequisites: undergraduate probability, linear algebra, differential equations. MATH 1010 is recommended.