@article{EJP804,
author = {Geoffrey Grimmett and Alexander Holroyd},
title = {Plaquettes, Spheres, and Entanglement},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {15},
year = {2010},
keywords = {entanglement; percolation; random sphere},
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.},
pages = {no. 45, 1415-1428},
issn = {1083-6489},
doi = {10.1214/EJP.v15-804},
url = {http://ejp.ejpecp.org/article/view/804}}