ACM 217: Probability in High Dimensions

Abstract

ACM 217 is a second-year graduate course on high-dimensional probability, designed for students in computing and mathematical sciences. We discuss phenomena that emerge from probability models with many degrees of freedom, tools for working with these models, and a selection of applications to computational mathematics. The Winter 2021 edition of ACM 217 is the fourth instantiation of a class that initially focused on concentration inequalities and that has expanded to include other topics in high-dimensional probability. This year, the course was more mathematical than some previous editions, with less attention to tools and applications. This slant may not serve applied students well, and it is likely that future versions of the course will strike a different balance between theory and practice. These lecture notes document ACM 217 as it was taught in Winter 2021. The notes are being transcribed by the students as part of their coursework, and they are edited lightly by the instructor. They are intended as a record for the students who have taken the course. Other readers should beware that this course is neither refined nor especially coherent. There is no warranty about correctness. Furthermore, these notes have been prepared using many sources and without appropriate scholarly citations.