Thumbnail
Access Restriction
Open

Author Grimmett, Geoffrey R. ♦ Holroyd, Alexander E. ♦ Kozma, Gady
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Percolation Finite Cluster Infinite Surface ♦ Corresponding Critical Point Pfin Satisfies ♦ Dual Plaquette Process ♦ Infinite Component ♦ Infinite Open Cluster Posse ♦ Associated Critical Point Psurf Satisfies ♦ Infinite Dual Surface ♦ Related Issue ♦ Bond Percolation ♦ Strict Inequality
Abstract Abstract. Two related issues are explored for bond percolation on Z d (with d ≥ 3) and its dual plaquette process. Firstly, for what values of the parameter p does the complement of the infinite open cluster possess an infinite component? The corresponding critical point pfin satisfies pfin ≥ pc, and strict inequality is proved when either d is sufficiently large, or d ≥ 7 and the model is sufficiently spread out. It is not known whether d ≥ 3 suffices. Secondly, for what p does there exist an infinite dual surface of plaquettes? The associated critical point psurf satisfies psurf ≥ pfin. 1.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article