Work

Recurrence and transience for non‐Archimedean and directed graphs

Year: 2025

Type: article

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.

Source: Mathematische Nachrichten

DOI: 10.1002/mana.70040

Authors: Matthias Keller, Anna Muranova

Institutions: University of Potsdam, University of Warmia and Mazury in Olsztyn

Language: English

Topic: advanced mathematical theories

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Narodowe Centrum Nauki

Award: G6284641632