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Percolation, Perimetry, Planarity

Percolation, perimetry, planarity
descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 31 Aug 2007Embargo end date: 01 Jan 2005Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Revista Matemática Iberoamericana, volume 23, pages 671-676 (issn: 0213-2230, eissn: 2235-0616, Copyright policy )
Authors: Kozma, Gady;

doi: 10.4171/rmi/508 , 10.48550/arxiv.math/0509235

arXiv: math/0509235

Percolation, Perimetry, Planarity

Abstract

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 .

Related Organizations
Keywords

Probability (math.PR), planar graph, Percolation, Interacting random processes; statistical mechanics type models; percolation theory, 60K35, 82B43, 05C10, Planar graphs; geometric and topological aspects of graph theory, percolation, 46B99, FOS: Mathematics, 46E35, duality, Mathematics - Combinatorics, isoperimetric dimension, 46E15, Combinatorics (math.CO), Mathematics - Probability

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    selected citations
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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 9
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
9
Average
Top 10%
Average
Green
gold