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# On Site Percolation in Random Quadrangulations of the Half-Plane

Jakob E. Björnberg (Institutionen för matematiska vetenskaper, matematisk statistik) ; S.Ö. Stefánsson
Journal of Statistical Physics (0022-4715). Vol. 160 (2015), 2, p. 336-356.

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.

Nyckelord: Peeling process , Percolation , Random quadrangulations

CPL Pubid: 219728

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# Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)