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Journal of Statistical Physics

, Volume 160, Issue 2, pp 336–356 | Cite as

On Site Percolation in Random Quadrangulations of the Half-Plane

  • Jakob E. Björnberg
  • Sigurdur Örn StefánssonEmail author
Article

Abstract

We study site percolation on uniform quadrangulations of the upper half plane. The main contribution is a method for applying Angel’s peeling process, in particular for analyzing an evolving boundary condition during the peeling. Our method lets us obtain rigorous and explicit upper and lower bounds on the percolation threshold \(p_\mathrm {c}\), and thus show in particular that \(0.5511\le p_\mathrm {c}\le 0.5581\). The method can be extended to site percolation on other half-planar maps with the domain Markov property.

Keywords

Percolation Random quadrangulations Peeling process 

Notes

Acknowledgments

This work was started while both authors were at Uppsala University in Sweden. We have benefited from discussions with Svante Janson, Takis Konstantopoulos, Pierre Nolin and Hermann Thorisson.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Jakob E. Björnberg
    • 1
  • Sigurdur Örn Stefánsson
    • 2
    Email author
  1. 1.Department of Mathematical SciencesChalmers and Gothenburg UniversityGöteborgSweden
  2. 2.Division of Mathematics, The Science InstituteUniversity of IcelandReykjavíkIceland

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