无限图的体积增长、谱与随机完备性
谱理论
2012-10-01 v2
摘要
我们研究局部有限图的体积增长、谱性质与随机完备性之间的联系。对于一类具有极弱球对称性的图，我们给出一个条件，该条件同时蕴含随机不完备性与谱的离散性。随后，我们利用这些图，对一般局部有限图的随机完备性及谱下界估计给出若干比较结果。
引用
@article{arxiv.1105.0395,
title = {Volume Growth, Spectrum and Stochastic Completeness of Infinite Graphs},
author = {Matthias Keller and Daniel Lenz and Radoslaw K. Wojciechowski},
journal= {arXiv preprint arXiv:1105.0395},
year = {2012}
}
备注
29 pages, 2 figures. Some references and definition environments added to the new version. Because of this, Lemmas 3.2 through 3.5 from Section 3 in the previous version are now Lemmas 3.3 through 3.6. Likewise, Lemmas 4.3 and 4.4 became Lemmas 4.4 and 4.5 and Corollary 5.2 is now Corollary 5.3 in the new version. Final version to appear in Math. Z