Networks with Complex Weights: Green Function and Power Series

Autor:	Anna Muranova, Wolfgang Woess
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	weighted graph network Green kernel recurrence transience Mathematics QA1-939
Zdroj:	Mathematics, Vol 10, Iss 5, p 820 (2022)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math10050820
Popis:	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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/40faff91c39e49f99bcb902d970c72e6 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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