Backbone scaling limit of the high-dimensional IIC: extended version
Probability
2017-06-12 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1706.02941,
title = {Backbone scaling limit of the high-dimensional IIC: extended version},
author = {Markus Heydenreich and Remco van der Hofstad and Tim Hulshof and Grégory Miermont},
journal= {arXiv preprint arXiv:1706.02941},
year = {2017}
}
Comments
This is a thorough revision of a previous submission, arXiv:1301.3486v2, which was retracted because of an error in the proof.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