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Communications on Pure and Applied Mathematics
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Absence of Infinite Cluster for Critical Bernoulli Percolation on Slabs

Absence of infinite cluster for critical Bernoulli percolation on slabs
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 09 Apr 2016Embargo end date: 01 Jan 2014 English Publisher:WileyJournal:Communications on Pure and Applied Mathematics, volume 69, pages 1,397-1,411 (issn: 0010-3640, eissn: 1097-0312, Copyright policy )Funded by:SNSF | Algèbre, Analyse, Géométr..., SNSF | Geometric and combinatori...
Authors: Duminil Hugo; Sidoravicius Vladas; Tassion Vincent;

doi: 10.1002/cpa.21641 , 10.48550/arxiv.1401.7130

arXiv: 1401.7130

Absence of Infinite Cluster for Critical Bernoulli Percolation on Slabs

Abstract

AbstractWe prove that for Bernoulli percolation on a graph , there is no infinite cluster at criticality, almost surely. The proof extends to finite‐range Bernoulli percolation models on ℤ2 that are invariant under ‐rotation and reflection.© 2016 Wiley Periodicals, Inc.

Related Organizations
Keywords

Applied Mathematics, General Mathematics, Probability (math.PR), 82B43, 60K35, 82B27, Percolation, Bernoulli percolation, FOS: Physical sciences, Interacting random processes; statistical mechanics type models; percolation theory, Mathematical Physics (math-ph), Phase transitions (general) in equilibrium statistical mechanics, FOS: Mathematics, Mathematics - Probability, Mathematical Physics

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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).
    		 18
    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.
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    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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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!
18
Top 10%
Top 10%
Top 10%
Green
bronze