论文标题
图形的随机完整性：有界的拉普拉斯人，内在指标，体积增长和曲率
Stochastic completeness of graphs: bounded Laplacians, intrinsic metrics, volume growth and curvature
论文作者
论文摘要
本文的目的是调查有关图形随机完整性的各种结果。特别是，我们介绍了各种随机完整性的公式，并讨论了如何在连续和离散设置中如何通过使用固有指标来解决唯一性类别和体积增长标准之间的差异。一路上，我们就几何学和分析意义上讨论了一些等效的界限概念。我们还讨论了随机完整性的各种曲率标准，并讨论了弱球形对称图如何建立结果的清晰度。
The goal of this article is to survey various results concerning stochastic completeness of graphs. In particular, we present a variety of formulations of stochastic completeness and discuss how a discrepancy between uniqueness class and volume growth criteria in the continuous and discrete settings was ultimately resolved via the use of intrinsic metrics. Along the way, we discuss some equivalent notions of boundedness in the sense of geometry and of analysis. We also discuss various curvature criteria for stochastic completeness and discuss how weakly spherically symmetric graphs establish the sharpness of results.
