Cylinders' percolation in three dimensions

• 成果类型: Article
• 署名作者: Hilario, M. R.; Sidoravicius, V.; Teixeira, A.
• 署名单位: Universidade Federal de Minas Gerais; University of Geneva; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0600-x
• 发表日期: 2015
• 页码: 613-642
• 关键词: vacant set; uniqueness

摘要

We study the complementary set of a Poissonian ensemble of infinite cylinders in , for which an intensity parameter controls the amount of cylinders to be removed from the ambient space. We establish a non-trivial phase transition, for the existence of an unbounded connected component of this set, as crosses a critical non-degenerate intensity . We moreover show that this complementary set percolates in a sufficiently thick slab, in spite of the fact that it does not percolate in any given plane of , regardless of the choice of .