Mathematics - Ph.D. / Sc.D.
(Massachusetts Institute of Technology, 2020)In this thesis, we develop a novel framework for investigating the lower tail behavior of the least singular value of random matrices - a subject which has been intensely studied in the past two decades. Our focus is on ...
(Massachusetts Institute of Technology, 2020)We study the global and local asymptotics of Macdonald processes, its degenerations, and related models using the method of difference operators. We focus on three applications. First, we consider random plane partitions ...