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Rank of Sparse Bernoulli Matrices
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abstract
Let $ A_n $ be an $n \times n$ random matrix with i.i.d Bernoulli($p$) entries. For a fixed positive integer $\beta$, suppose $p$ satisfies $$ \frac{ \log(n) }{ n } \le p \le c_\beta $$ where $c_\beta \in ( 0, 1/2 )$ is a $\beta$-dependentvalue. For $t \ge 0$, $$ \mathbb{P} \left\{ s_{ n - \beta + 1}(A) \le t n^{-2\beta + \mathfrak{n}(1) }(pn)^{-7} \right\} = t + ( 1 + o_\mathfrak{n}(1) ) \mathbb{P} \bigg\{ \mbox{either $\beta$ rows or $\beta$ columns of $A_n$ equal $\vec{0}$} \bigg\}. $$
Forward citations
Cited by 1 Pith paper
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Accelerating Randomized Algorithms for Low-Rank Matrix Approximation
Sparse random test matrices can replace dense Gaussian matrices in the farPCA low-rank approximation algorithm, preserving accuracy while reducing computation time.
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