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Discrete Math

Littlewood-Offord-Erdos type inequalities for polynomials of random variables

Van Vu, Yale University

Location:  Hill 705
Date & time: Monday, 27 March 2017 at 2:00PM -

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.

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