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Algorithms & Randomness Center (ARC)
Konstantin Tikhomirov
Monday, March 4, 2019
Klaus 1116E - 11:00 am
Title: Singularity of Bernoulli random matrices
Abstract: Abstract: Let X_1,X_2,...,X_n be independent random vectors uniformly distributed on vertices of the n-dimensional cube [-1,1]^n. What is the probability that the vectors are linearly dependent? The question has been studied in the literature since 1960-es, and it was conjectured that
P{the vectors are linearly dependent}=(0.5+o(1))^n.
In this talk, we will discuss a proof of this conjecture based on analysis of the associated random matrix.
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