### Rutgers Discrete Mathematics Seminar

Title: Littlewood-Offord-Erdos Type Inequalities for Polynomials of Random Variables

Speaker: **Van Vu**, Yale University

Date: Monday, March 27, 2017 2:00 pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:
Let Q = a_1x_1 + ....+a_n x_n where a_i are non-zero real numbers, and x_i are +-1 random variables. A classical result of Littlewood-Offord-Erdos showed that Pr (Q=0) is O( n^{-1/2} ). We are going to discuss the general case when Q is a polynomial (in the x_i) with arbitrary degree. We will present several new results/methods together with applications in various fields and a few open questions.