Singularity of random Bernoulli matrices

2018/12/21 by Tikhomirov, Konstantin · 7 citations
#Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1812.09016

Abstract

For each n, let M_n be an n× n random matrix with independent ± 1 entries. We show that \mathbb P\M_n is singular\=(1/2+o_n(1))ⁿ, which settles an old problem. Some generalizations are considered.

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