Open Access
Translator Disclaimer
2010 Plaquettes, Spheres, and Entanglement
Geoffrey Grimmett, Alexander Holroyd
Author Affiliations +
Electron. J. Probab. 15: 1415-1428 (2010). DOI: 10.1214/EJP.v15-804

Abstract

The high-density plaquette percolation model in $d$ dimensions contains a surface that is homeomorphic to the $(d-1)$-sphere and encloses the origin. This is proved by a path-counting argument in a dual model. When $d=3$, this permits an improved lower bound on the critical point $p_e$ of entanglement percolation, namely $p_e\geq \mu^{-2}$ where $\mu$ is the connective constant for self-avoiding walks on $\mathbb{Z}^3$. Furthermore, when the edge density $p$ is below this bound, the radius of the entanglement cluster containing the origin has an exponentially decaying tail.

Citation

Download Citation

Geoffrey Grimmett. Alexander Holroyd. "Plaquettes, Spheres, and Entanglement." Electron. J. Probab. 15 1415 - 1428, 2010. https://doi.org/10.1214/EJP.v15-804

Information

Accepted: 19 September 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1229.60107
MathSciNet: MR2721052
Digital Object Identifier: 10.1214/EJP.v15-804

Subjects:
Primary: 60K35
Secondary: 82B20

Keywords: entanglement , percolation , random sphere

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.15 • 2010
Back to Top