Any infinite graph has site and bond percolation critical probabilities satisfying $p_c^{ site}\geq p_c^{ bond}$. The strict version of this inequality holds for many, but not all, infinite graphs. In this paper, the class of graphs for which the strict inequality holds is extended to a continuum percolation model. In Gilbert's graph with supercritical density on the Euclidean plane, there is almost surely a unique infinite connected component. We show that on this component $p_c^{ site} > p_c^{ bond}$. This also holds in higher dimensions.
Categories: math.PR