高维 IIC 骨架的标度极限
概率论
2013-10-10 v2
摘要
我们在长程和有限程设置下，分别确定了高维初生无穷簇（IIC）骨架的标度极限。在有限程设置下，该标度极限为布朗运动；在长程设置下，该标度极限为稳定运动。证明依赖于一种新颖的渗流花边展开，该展开类似于 Brydges 和 Spencer 在 1985 年提出的自回避游走的原始展开。这一展开本身也颇具研究价值。
引用
@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}
}
备注
Withdrawn because certain correction terms that arise in the Lace expansion of Section 3 were not identified and taken into account in the subsequent derivation.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