Anti-Concentration, Random Matrices, and Random Functions

点击翻译按钮获取中文摘要

The goal of the project is to study problems concerning distribution of discrete random variables, such as random polynomials, random sums, and random matrices. These problems have many connections to other parts of mathematics, as well as applications in statistics and machine learning. The PI aims to continue his development of a theory of anti-concentration. This theory has found applications in various areas of mathematics, including probability, numercial linear algebra, and complexity theory. He will also investigate an old and natural problem of Erdos and Moser concerning sum-avoiding sets in the non-abelian setting, following his recent work with T. Tao concerning the abelian case. In another part of the proposal, the PI proposes to study several problems concerning random matrices and random functions. Many of these problems are very basic and easy to state, but have been major challenges to the mathematics community for a long time, and progress on them has been made very recently.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.