具有复杂权重的网络：格林函数和幂级数
Networks with complex weights: Green function and power series
AI总结：
本文研究了具有复数权重的有限和无限网络中的格林函数及其相关核，通过与可逆马尔可夫链的比较，展示了复数权重下的瞬态和复发性概念的推广。
摘要：
我们引入了有限和无限网络中的格林函数及其相关核的类比，这些网络的边权重为具有正实部的复数电导率。我们提供了与对应可逆马尔可夫链相同核的比较结果，即边权重为正数的情况。在适当条件下，这些结果导致了表达这些核的矩阵幂级数的比较。我们展示了瞬态和复发性的概念通过解析延拓扩展到复数权重的情况，即使网络是无限的。因此，许多已知于马尔可夫链的方法也扩展到了该设置。
英文摘要：
We introduce a Green function and analogues of other related kernels for finite and infinite networks whose edge weights are complex-valued admittances with positive real part. We provide comparison results with the same kernels associated with corresponding reversible Markov chains, i.e., where the edge weights are positive. Under suitable conditions, these lead to comparison of series of matrix powers which express those kernels. We show that the notions of transience and recurrence extend by analytic continuation to the complex-weighted case even when the network is infinite. Thus, a variety of methods known for Markov chains extend to that setting.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
