再看随机锥体的阈值现象

Pub Date : 2021-03-21 DOI:10.1556/012.2021.01513
D. Hug, R. Schneider
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引用次数: 6

摘要

在随机几何中,有几个高维阈值现象的例子:当某些参数超过临界值时,某些期望的极限的行为突然改变。本文继续研究当周围空间的维数增加到无穷大时多面体随机锥体的期望面数。重点是观察到的阈值现象的临界值,以及差而不是商的阈值现象。
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Another Look at Threshold Phenomena for Random Cones
In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passes through a critical value. This note continues the investigation of the expected face numbers of polyhedral random cones, when the dimension of the ambient space increases to infinity. In the focus are the critical values of the observed threshold phenomena, as well as threshold phenomena for differences instead of quotients.
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