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.

中文翻译：

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图的随机完整性：有界拉普拉斯算子，本征度量，体积增长和曲率

本文的目的是调查与图的随机完整性有关的各种结果。特别是，我们提出了各种随机完整性的表述，并讨论了如何通过使用内在指标最终解决连续性和离散性环境中唯一性类别与数量增长标准之间的差异。在此过程中，我们讨论了几何学和分析意义上的一些等效的有界概念。我们还讨论了随机完整性的各种曲率准则，并讨论了弱球对称图如何建立结果的清晰度。