Springer Online Journal Archives 1860-2000
Abstract We show that for a long range percolation model with exponentially decaying connections, the limit of critical values of any sequence of long range percolation models approaching the original model from below is the critical value for the original long range percolation model. As an interesting corollary, this implies that if a long range percolation model with exponential connections is supercritical, then it still percolates even if all long bonds are removed. We also show that the percolation probability is continuous (in a certain sense) in the supercritical regime for long range percolation models with exponential connections.
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