On Site Percolation in Random Quadrangulations of the Half-Plane Journal article, 2015

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 $$p_\mathrm {c}$$pc, and thus show in particular that $$0.5511\le p_\mathrm {c}\le 0.5581$$0.5511≤pc≤0.5581. The method can be extended to site percolation on other half-planar maps with the domain Markov property.

Percolation

Peeling process

Author

Jakob Björnberg

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Journal of Statistical Physics

0022-4715 (ISSN) 1572-9613 (eISSN)

Vol. 160 2 336-356

Mathematics

DOI

10.1007/s10955-015-1256-3