Combinatorics and Discrete Probability Seminar
Matthew Kwan
IST Austria
Resolution of the Quadratic Littlewood-Offord problem
Abstract: Consider a quadratic polynomial $Q(\xi_{1},\dots,\xi_{n})$ of a random binary sequence $\xi_{1},\dots,\xi_{n}$. To what extent can $Q(\xi_{1},\dots,\xi_{n})$ concentrate on a single value? This is a quadratic version of the classical Littlewood-Offord problem; it was was popularised by Costello, Tao and Vu in their study of symmetric random matrices, and has since become a rich source of connections between combinatorics, probability and computer science. In this talk we will discuss a new essentially optimal bound for the quadratic Littlewood-Offord problem, as conjectured by Nguyen and Vu. Joint work with Lisa Sauermann.
Wednesday February 14, 2024 at 3:00 PM in 636 SEO