Recurrence and transience for non-Archimedean and directed graphs

Published 25 Jun 2024 in math.CO, math-ph, math.AP, math.MP, math.PR, and math.SP | (2406.17344v1)

Abstract: We introduce the notion of recurrence and transience for graphs over non-Archimedean ordered field. To do so we relate these graphs to random walks of directed graphs over the reals. In particular, we give a characterization of the real directed graphs which can arise is such a way. As a main result, we give characterization for recurrence and transience in terms of a quantity related to the capacity.

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