Grimmett, Geoffrey R.; Holroyd, Alexander E. Plaquettes, spheres, and entanglement. (English) Zbl 1229.60107 Electron. J. Probab. 15, Paper No. 45, 1415-1428 (2010). The authors consider the plaquette percolation model, that is a natural dual to bond percolation in two and more dimensions, and prove that 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 bond percolation model. Reviewer: Nasir N. Ganikhodjaev (Kuantan) Cited in 11 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics Keywords:entanglement; percolation; random sphere PDF BibTeX XML Cite \textit{G. R. Grimmett} and \textit{A. E. Holroyd}, Electron. J. Probab. 15, Paper No. 15, 1415--1428 (2010; Zbl 1229.60107) Full Text: DOI EMIS arXiv