Non-triviality of the vacancy phase transition for the Boolean model

作者：Penrose Mathew D^*

来源：Electronic Communications in Probability, 2018, 23(0): 49.

DOI：10.1214/18-ECP153

• percolation
• Poisson process
• vacant region
• critical value

In the spherical Poisson Boolean model, one takes the union of random balls centred on the points of a Poisson process in Euclidean d-space with d >= 2. We prove that whenever the radius distribution has a finite d-th moment, there exists a strictly positive value for the intensity such that the vacant region percolates.

• 出版日期2018