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- W2008685166 abstract "Under a certain assumption (which is satisfied whenever there is a dense infinite cluster in the half-space), we prove a differential inequality for the infinite-cluster density, ${P}_{ensuremath{infty}}(p)$, in Bernoulli percolation. The principal implication of this result is that if ${P}_{ensuremath{infty}}(p)$ vanishes with critical exponent $ensuremath{beta}$, then $ensuremath{beta}$ obeys the mean-field bound $ensuremath{beta}<~1$. As a corollary, we also derive an inequality relating the backbone density, the truncated susceptibility, and the infinite-cluster density." @default.
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- W2008685166 date "1986-04-21" @default.
- W2008685166 modified "2023-09-26" @default.
- W2008685166 title "Inequality for the Infinite-Cluster Density in Bernoulli Percolation" @default.
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- W2008685166 doi "https://doi.org/10.1103/physrevlett.56.1619" @default.
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