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- W3089354414 abstract "Consider an $ntimes n$ random matrix $A_n$ with i.i.d Bernoulli($p$) entries. In a recent result of Litvak-Tikhomirov, they proved the conjecture $$ mathbb{P}{mbox{$A_n$ is singular}}=(1+o_n(1)) mathbb{P}big{mbox{either a row or a column of $A_n$ equals zero}big}. $$ for $ Cfrac{log(n)}{n} le p le frac{1}{C}$ for some large constant $C>1$. In this paper, we setted this conjecture in the sparse regime when $p$ satisfies $$ 1 le liminf_{nrightarrow infty} frac{pn}{log(n)} le limsup_{nrightarrow infty} frac{pn}{log(n)} < + infty. $$" @default.
- W3089354414 created "2020-10-08" @default.
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- W3089354414 date "2020-09-29" @default.
- W3089354414 modified "2023-09-27" @default.
- W3089354414 title "Singularity of Bernoulli matrices in the sparse regime $pn = O(log(n))$" @default.
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