AI 中文总结
研究一类含长程跳跃的随机电导模型，通过展示离散非局部散度形式算子的锚定纳什不等式，用非一致椭圆狄氏型控制函数\(L^{2}\)范数，进而给出对角热核上界，成果适用于包括整数格等的一类图。
AI 中文摘要
我们展示了具有退化权重的离散非局部散度形式算子的纳什不等式的锚定版本。它们允许通过非一致椭圆的狄氏型来控制函数的\(L^{2}\)范数。然后我们用它们为一类具有退化跳跃率且允许长程跳跃的随机电导模型提供对角热核上界。结果是在包括整数格和可能相关的超临界渗流簇的一类图上建立的。
英文摘要
We show anchored versions of the Nash inequality for discrete non-local divergence-form operators with degenerate weights. They allow to control the $L^{2}$-norm of a function by Dirichlet forms that are not uniformly elliptic. We then use them to provide on-diagonal heat kernel upper bounds for a class of random conductance models with degenerate jump rates allowing long-range jumps. The results are established on a class of graphs including the integer lattice and possibly correlated supercritical percolation clusters.
Comments36 pages
