Percolation on random Johnson-Mehl tessellations and related models

Erratum: Percolation on random Johnson-Mehl tessellations and related models

We correct a simple error in Percolation on random Johnson-Mehl tessellations and related models, Probability Theory and Related Fields 140 (2008), 417-468. (See also arXiv:math/0610716)

内部变半径随机覆盖与 Johnson-Mehl 覆盖时间

Random coverage from within with variable radii, and Johnson-Mehl cover times

本文研究了紧致平面区域 $A$ 的 Johnson-Mehl 镶嵌完成时间，推导出包含边界效应的渐近覆盖概率，并推广至高维及随机半径颗粒的 Poisson Boolean 模型。

A Harris-Kesten theorem for confetti percolation

Percolation properties of the dead leaves model, also known as confetti percolation, are considered. More precisely, we prove that the critical probability for confetti percolation with square-shaped leaves is 1/2. This result is related to a question of Benjamini and Schramm concerning disk-shaped leaves and can be seen as a variant of the Harris-Kesten theorem for bond percolation. The proof is based on techniques developed by Bollobás and Riordan to determine the critical probability for Voronoi and Johnson-Mehl percolation.