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Igor Rivin
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Well, the probability that the kernel of $M$ is nontrivial is bounded above by around $(3/4)^n,$ by Tao-Vu (J. Amer. Math. Soc. 20 (2007), 603-628), so there is that. If $m<n,$ the probability is certainly smaller than that...

Well, the probability that the kernel of $M$ is nontrivial is bounded above by around $(3/4)^n,$ by Tao-Vu (J. Amer. Math. Soc. 20 (2007), 603-628), so there is that. If $m<n,$ the probability is certainly smaller than that...

Well, the probability that the kernel of $M$ is nontrivial is bounded above by around $(3/4)^n,$ by Tao-Vu (J. Amer. Math. Soc. 20 (2007), 603-628), so there is that.

added a comment on $m<n.$
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Igor Rivin
  • 96.4k
  • 11
  • 153
  • 366

Well, the probability that the kernel of $M$ is nontrivial is bounded above by around $(3/4)^n,$ by Tao-Vu (J. Amer. Math. Soc. 20 (2007), 603-628), so there is that. If $m<n,$ the probability is certainly smaller than that...

Well, the probability that the kernel of $M$ is nontrivial is bounded above by around $(3/4)^n,$ by Tao-Vu (J. Amer. Math. Soc. 20 (2007), 603-628), so there is that...

Well, the probability that the kernel of $M$ is nontrivial is bounded above by around $(3/4)^n,$ by Tao-Vu (J. Amer. Math. Soc. 20 (2007), 603-628), so there is that. If $m<n,$ the probability is certainly smaller than that...

Source Link
Igor Rivin
  • 96.4k
  • 11
  • 153
  • 366

Well, the probability that the kernel of $M$ is nontrivial is bounded above by around $(3/4)^n,$ by Tao-Vu (J. Amer. Math. Soc. 20 (2007), 603-628), so there is that...