论文标题
关于随机多面体的音量阈值的注释
A note on volume thresholds for random polytopes
论文作者
论文摘要
我们研究通过从给定分布中取出独立分布点的凸壳产生的随机多型的预期体积。我们表明，对于在凸体支撑的对数 - 符合分布中，我们至少需要指数级的许多（在维度）样本中，以使预期体积很重要，并且当它们的凹入参数为正时，超过指数的许多样品就足以进行凹度。
We study the expected volume of random polytopes generated by taking the convex hull of independent identically distributed points from a given distribution. We show that for log-concave distributions supported on convex bodies, we need at least exponentially many (in dimension) samples for the expected volume to be significant and that super-exponentially many samples suffice for concave measures when their parameter of concavity is positive.
