Backbone scaling limit of the high-dimensional IIC: extended version
arXiv:1706.02941
Abstract
We identify the scaling limit of the backbone of the high-dimensional incipient infinite cluster (IIC), both in the finite-range and the long-range setting. In the finite-range setting, this scaling limit is Brownian motion, in the long-range setting, it is a stable motion. The proof relies on a novel lace expansion that keeps track of the number of pivotal bonds.
This is a thorough revision of a previous submission, arXiv:1301.3486v2, which was retracted because of an error in the proof. The results presented here are the same as those claimed in arXiv:1301.3486v2 (modulo a few details), but large parts of the proof are different. 86 pages, 46 figures