Backbone scaling limit of the high-dimensional IIC
Probability
2013-10-10 v2
Abstract
We identify the scaling limit of the backbone of the high-dimensional incipient infinite cluster (IIC), both in the long- as well as in the finite-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 for percolation that resembles the original expansion for self-avoiding walks by Brydges and Spencer in 1985. This expansion is interesting in its own right.
Keywords
Cite
@article{arxiv.1301.3486,
title = {Backbone scaling limit of the high-dimensional IIC},
author = {Markus Heydenreich and Remco van der Hofstad and Tim Hulshof and Grégory Miermont},
journal= {arXiv preprint arXiv:1301.3486},
year = {2013}
}
Comments
Withdrawn because certain correction terms that arise in the Lace expansion of Section 3 were not identified and taken into account in the subsequent derivation. A new version with these correction terms included is in preparation