We establish two-sided heat kernel estimates for random conductance models with non-uniformly elliptic (possibly degenerate) stable-like jumps on graphs. These are long range counterparts of well known two-sided Gaussian heat kernel estimates by M.T. Barlow for nearest neighbor (short range) random walks on the supercritical percolation cluster. Unlike the cases for nearest neighbor conductance models, the idea through parabolic Harnack inequalities does not work, since even elliptic Harnack inequalities do not hold in the present setting. As an application, we establish the local limit theorem for the models.

中文翻译：

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具有稳定跳跃的随机电导模型：热核估计和 Harnack 不等式

我们为随机电导模型建立了两侧热核估计，在图上具有非均匀椭圆（可能退化）稳定的跳跃。这些是 MT Barlow 对超临界渗透簇上的最近邻（短程）随机游动进行的众所周知的两侧高斯热核估计的长程对应物。与最近邻电导模型的情况不同，通过抛物线 Harnack 不等式的想法不起作用，因为即使是椭圆形 ​​Harnack 不等式在当前设置中也不成立。作为应用，我们建立了模型的局部极限定理。