Let μ be an even compactly supported Borel probability measure on the real line. For every N > n consider N independent random vectors X 1, ..., X N in ℝ n , with independent coordinates having distribution μ. We establish a sharp threshold for the volume of the random polytope K N ≔ conv{X 1, ..., X N }, provided that the Legendre transform λ of the cumulant generating function of μ satisfies the condition
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机译：令μ为实线上的甚至得到紧密支持的Borel概率度量。对于每个N> n，请考虑ℝ n 中的N个独立的随机向量X 1 ，...，X N ，其独立坐标具有分布μ 。我们为随机多态性K N ≔conv {X 1 ，...，X N }的体积建立了一个清晰的阈值μ的累积量生成函数的勒让德变换λ满足条件
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