论文标题
具有复杂权重的网络：绿色功能和功率系列
Networks with complex weights: Green function and power series
论文作者
论文摘要
我们引入了其他相关内核的绿色函数和类似物，用于有限和无限网络，其边缘权重是复杂的值，具有积极的实际部分。我们提供了与与相应的可逆马尔可夫链相同的内核，即边缘重量为正的情况。在适当的条件下，这些导致比较表达这些内核的一系列矩阵幂。我们表明，即使网络是无限的，瞬态和复发的概念也会通过分析延续到复杂的加权情况。因此，马尔可夫链已知的多种方法扩展到该设置。
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.
