Revista Matemática Iberoamericana


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Volume 23, Issue 2, 2007, pp. 671–676
DOI: 10.4171/RMI/508

Published online: 2007-08-31

Percolation, Perimetry, Planarity

Gady Kozma[1]

(1) Weizmann Institute of Science, Rehovot, Israel

Let $G$ be a planar graph with polynomial growth and isoperimetric dimension bigger than $1$. Then the critical $p$ for Bernoulli percolation on $G$ satisfies $p_{c} < 1$.

Keywords: Percolation, isoperimetric dimension, planar graph, duality

Kozma Gady: Percolation, Perimetry, Planarity. Rev. Mat. Iberoamericana 23 (2007), 671-676. doi: 10.4171/RMI/508