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 $$p_\mathrm {c}$$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.
| Original language | English |
|---|---|
| Pages (from-to) | 336-356 |
| Number of pages | 21 |
| Journal | Journal of Statistical Physics |
| Volume | 160 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 26 Jul 2015 |
Bibliographical note
Funding Information: The research of jeb is supported by the Knut and Alice Wallenberg Foundation. Publisher Copyright: © 2015, Springer Science+Business Media New York.Other keywords
- Peeling process
- Percolation
- Random quadrangulations