Stability and instability of Gaussian heat kernel estimates for random walks among time-dependent conductances
Stability and instability of Gaussian heat kernel estimates for random walks among time-dependent conductances
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DOI：
10.1214/15-ecp4347
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发表时间：
2015-06
期刊：
影响因子：
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通讯作者：
Ruojun Huang;T. Kumagai
中科院分区：
文献类型：
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作者：
Ruojun Huang;T. Kumagai
我们考虑时间相关电导之间的时间相关随机游动。对于离散时间随机游走，我们表明，与时间无关的情况不同，两侧高斯热核估计在扰动下不稳定。这通过给出均匀椭圆时间相关电导中 Z 上的弹道和瞬态时间相关随机游走的示例来证明。对于连续时间随机游走，我们展示了当保持时间为 i.i.d 时的不稳定性。 exp(1)，相反，我们证明了当保持时间随地点变化时的稳定性，使得基本测度是统一测度。
We consider time-dependent random walks among time-dependent conductances. For discrete time random walks, we show that, unlike the time-independent case, two-sided Gaussian heat kernel estimates are not stable under perturbations. This is proved by giving an example of a ballistic and transient time-dependent random walk on Z among uniformly elliptic time-dependent conductances. For continuous time random walks, we show the instability when the holding times are i.i.d. exp(1), and in contrast, we prove the stability when the holding times change by sites in such a way that the base measure is a uniform measure.