论文标题
Haagerup在polydisc切片时的相变
Haagerup's phase transition at polydisc slicing
论文作者
论文摘要
我们在三维欧几里德球体上均匀的独立随机矢量和统一的幅度的第二刻之间建立了急剧的比较不等式。这提供了Oleszkiewicz-Pelczyńskipolydiscing切片结果的概率扩展。与实际情况相比，当p-norm恢复体积时，haagerup型相变的恰好发生。我们还以较高的维度获得了部分结果。
We establish a sharp comparison inequality between the negative moments and the second moment of the magnitude of sums of independent random vectors uniform on three-dimensional Euclidean spheres. This provides a probabilistic extension of the Oleszkiewicz-Pelczyński polydisc slicing result. The Haagerup-type phase transition occurs exactly when the p-norm recovers volume, in contrast to the real case. We also obtain partial results in higher dimensions.
