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A d-dimensional contact process is a simplified model for the spread of a biological organism or an infection on the lattice Zd. At each time t 2:: 0, every point of the lattice (or site) is either infected or healthy. As time passes, a healthy site is infected with Poisson rate A by each of its 2d immediate neighbors which is itself infected; an infected site recovers and becomes healthy with Poisson rate 1. The processes involved are independent. If the process starts with a set A C Zd ofdoi:10.3150/bj/1066418877 fatcat:zhab34kiivaxvnimbwotbnbgxy