Volume growth and stochastic completeness of graphs
Volume growth and stochastic completeness of graphs
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DOI：
10.1090/s0002-9947-2013-05930-2
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发表时间：
2012-01
影响因子：
1.3
通讯作者：
M. Folz
中科院分区：
文献类型：
--
作者：
M. Folz
给定可变速度的随机行走的加权图和一个度量适应的随机行走的结构，我们构建一个布朗运动的密切相关的度量图的行为类似于VSRW和相关的内在度量具有某些理想的性质。本文计算了布朗运动在具有不同边长、跳导和边密度的度量图上的跳概率和跳时矩。我们使用这些结果与Sturm定理随机完整性，或非爆炸性，局部Dirichlet空间，以证明急剧的体积增长标准，适应度量的随机完整性的图形。
Given the variable-speed random walk on a weighted graph and a metric adapted to the structure of the random walk, we construct a Brownian motion on a closely related metric graph which behaves similarly to the VSRW and for which the associated intrinsic metric has certain desirable properties. Jump probabilities and moments of jump times for Brownian motion on metric graphs with varying edge lengths, jump conductances, and edge densities are computed. We use these results together with a theorem of Sturm for stochastic completeness, or non-explosiveness, on local Dirichlet spaces to prove sharp volume growth criteria in adapted metrics for stochastic completeness of graphs.