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Presented By: Department of Mathematics

Colloquium Series Seminar

Singularity of random Bernoulli matrices

Let X_1,X_2,...,X_n be n mutually independent random vectors where each vector is uniformly distributed on vertices of the standard cube [-1,1]^n. What is the probability that the vectors are linearly dependent? Starting from a pioneering work of Komlos in the 1960-es, the question has attracted considerable attention. It has been conjectured that the probability is of the order (1/2+o(1))^n. Until recently, the best known upper estimate on the probability was (1/sqrt{2}+o(1))^n, due to Bourgain, Vu and Wood.
In this talk, I will discuss a positive resolution of the conjecture, as well as some further developments. Speaker(s): Konstantin Tikhomirov (Georgia Tech)

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