On the singularity probability of random Bernoulli matrices

Terence Tao; Van Vu

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On the singularity probability of random Bernoulli matrices

Terence Tao·Van Vu

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Abstract

Let $n$ be a large integer and $M_n$ be a random $n$ by $n$ matrix whose entries are i.i.d. Bernoulli random variables (each entry is $\pm 1$ with probability 1/2). We show that the probability that $M_n$ is singular is at most $(3/4 +o(1))^n$, improving an earlier estimate of Kahn, Komlós and Szemerédi, as well as earlier work by the authors. The key new ingredient is the applications of Freiman type inverse theorems and other tools from additive combinatorics.

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BibTeX RIS

Terence Tao, Van Vu. 2008-08-06. On the singularity probability of random Bernoulli matrices. https://arxiv.org/abs/math/0501313

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