1993/01/01 by Robert M. Burton, Ronald W. J. Meester · 1 citation
paper · doi:10.1002/rsa.3240040205
Abstract We consider a continuum percolation model in ℝ d , d ⩾ 1 in which any two points of a stationary point process are connected with a probability which decays exponentially in the distance between the points. We give sufficient conditions for the (non)‐existence of a phase transition. We also give examples of processes which show that it is impossible to write down a theorem which relates the critical parameter value of a process to its density. Finally, we show that uniqueness of the infinite cluster is still valid in this general setting. © 1993 John Wiley & Sons, Inc.