Variance asymptotics and scaling limits for Gaussian polytopes

被引：14

作者：

Calka, Pierre ^{[1
]}

Yukich, J. E. ^{[2
]}

机构：

[1] Univ Rouen, Lab Math Raphael Salem, F-76801 St Etienne, France

[2] Lehigh Univ, Dept Math, Bethlehem, PA 18015 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2015年 / 163卷 / 1-2期

关键词：

Random polytopes; Parabolic germ-grain models; Convex hulls of Gaussian samples; Poisson point processes; Burgers' equation; CONVEX HULLS; POINTS; THEOREMS;

D O I：

10.1007/s00440-014-0592-6

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let K-n be the convex hull of i.i.d. random variables distributed according to the standard normal distribution on . We establish variance asymptotics as for the re-scaled intrinsic volumes and -face functionals of , , resolving an open problem (Weil and Wieacker, Handbook of Convex Geometry, vol. B, pp. 1391-1438. North-Holland/Elsevier, Amsterdam, 1993). Variance asymptotics are given in terms of functionals of germ-grain models having parabolic grains with apices at a Poisson point process on with intensity . The scaling limit of the boundary of as converges to a festoon of parabolic surfaces, coinciding with that featuring in the geometric construction of the zero viscosity solution to Burgers' equation with random input.

引用

页码：259 / 301

页数：43

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