
Open access
Date
2014Type
- Journal Article
Citations
Cited 20 times in
Web of Science
Cited 23 times in
Scopus
ETH Bibliography
yes
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Abstract
We construct the uniform infinite planar map (UIPM), obtained as the n→∞ local limit of planar maps with n edges, chosen uniformly at random. We then describe how the UIPM can be sampled using a "peeling" process, in a similar way as for uniform triangulations. This process allows us to prove that for bond and site percolation on the UIPM, the percolation thresholds are pbondc=1/2 and psitec=2/3 respectively. This method also works for other classes of random infinite planar maps, and we show in particular that for bond percolation on the uniform infinite planar quadrangulation, the percolation threshold is pbondc=1/3. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000079462Publication status
publishedExternal links
Journal / series
Electronic Journal of ProbabilityVolume
Pages / Article No.
Publisher
Institute of Mathematical StatisticsSubject
Random map; UIPQ; Percolation threshold; Peeling processOrganisational unit
02004 - Mathematik Dep. Einrichtungen
Related publications and datasets
Is new version of: https://arxiv.org/abs/1302.2851
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Show all metadata
Citations
Cited 20 times in
Web of Science
Cited 23 times in
Scopus
ETH Bibliography
yes
Altmetrics