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Recurrence and transience for non‐Archimedean and directed graphs

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  • Matthias Keller
  • Anna Muranova

Abstract

We introduce notions of recurrence and transience for graphs over a non‐Archimedean ordered field. To achieve this, we establish a connection between these graphs and random walks on directed graphs over the reals. In particular, we give a characterization of the real directed graphs which can arise in such a way. As a main result, we give characterization for recurrence and transience in terms of a quantity related to the capacity.

Suggested Citation

  • Matthias Keller & Anna Muranova, 2025. "Recurrence and transience for non‐Archimedean and directed graphs," Mathematische Nachrichten, Wiley Blackwell, vol. 298(10), pages 3307-3330, October.
  • Handle: RePEc:bla:mathna:v:298:y:2025:i:10:p:3307-3330
    DOI: 10.1002/mana.70040
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