LARGE FACES IN POISSON HYPERPLANE MOSAICS

• 成果类型: Article
• 署名作者: Hug, Daniel; Schneider, Rolf
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology; University of Freiburg
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP510
• 发表日期: 2010
• 页码: 1320-1344
• 关键词: large cells; tessellations

摘要

A generalized version of a well-known problem of D. G. Kendall states that the zero cell of a stationary Poisson hyperplane tessellation in R(d), under the condition that it has lame volume, approximates with high probability a certain definite shape, which is determined by the directional distribution of the underlying hyperplane process. This result is extended here to typical k-faces of the tessellation, for k is an element of {2, ... , d - 1}. This requires the additional condition that the direction of the face be in a sufficiently small neighbourhood of a given direction.