On the Volume of the Zero Cell of a Class of Isotropic Poisson Hyperplane Tessellations

Author:

Hörrmann Julia,Hug Daniel

Abstract

We study a parametric class of isotropic but not necessarily stationary Poisson hyperplane tessellations in n-dimensional Euclidean space. Our focus is on the volume of the zero cell, i.e. the cell containing the origin. As a main result, we obtain an explicit formula for the variance of the volume of the zero cell in arbitrary dimensions. From this formula we deduce the asymptotic behaviour of the volume of the zero cell as the dimension goes to ∞.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Statistics and Probability

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Glasslike caging with random planes;Physical Review E;2024-02-22

2. Face numbers of high-dimensional Poisson zero cells;Proceedings of the American Mathematical Society;2022-08-18

3. Stochastic Geometry to Generalize the Mondrian Process;SIAM Journal on Mathematics of Data Science;2022-05-02

4. Weak convergence of the intersection point process of Poisson hyperplanes;Annales de l'Institut Henri Poincaré, Probabilités et Statistiques;2022-05-01

5. Thin-shell concentration for zero cells of stationary Poisson mosaics;Advances in Applied Mathematics;2020-06

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3