Math 790 (Graduate minicourse): The Superconcentration Phenomenon, Spring 2026

Instructor: Nicholas Cook
WF 1:25--2:40, Feb 11--Mar 06, Physics 119
(plus a 9th lecture on some Monday TBD)

The concentration of measure phenomenon is a central concept in probability and high-dimensional geometry, with countless applications since it was first appreciated in the 70s. More recently it has been appreciated that certain important random processes concentrate at a scale significantly smaller than the (already surprisingly small) scale provided by "off-the-shelf" concentration inequalities. Examples include eigenvalues of random matrices, first-passage percolation, spin glasses, and Gaussian polymer models. A set of interrelated phenomena have been identified that help to understand when to expect such "superconcentration". Lectures will draw from Chatterjee's monograph and some more recent papers.

Credit will be based on attendance and completion of some exercises.

References:
Superconcentration and Related Topics. Sourav Chatterjee. Available at Springerlink.