An improvement of Harris' theorem on percolation is obtained; it implies relations between critical points of matching graphs of the type of the one stated by Essam and Sykes. As another consequence, it is proved that the percolation probability, as a function of the probability of occupation of a given site, is infinitely differentiable, except at most in the critical point. © 1978 Springer-Verlag.
CITATION STYLE
Russo, L. (1978). A note on percolation. Zeitschrift Für Wahrscheinlichkeitstheorie Und Verwandte Gebiete, 43(1), 39–48. https://doi.org/10.1007/BF00535274
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