Matrix rigidity of random Toeplitz matrices

Abstract

We prove that random <i>n</i>-by-<i>n</i> Toeplitz (alternatively Hankel) matrices over F<sub>2</sub> have rigidity &#x3A9;(<i>n</i><sup>3</sup>/<i>r</i><sup>2</sup>log<i>n</i>) for rank <i>r</i> &#x2265; &#x221A;<i>n</i>, with high probability. For <i>r</i> = <i>o</i>(<i>n</i>/log<i>n</i> &#xB7; loglog<i>n</i>), this improves over the &#x3A9;(<i>n</i><sup… (More)
DOI: 10.1007/s00037-016-0144-9

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