Recurrence and transience for non-Archimedean and directed graphs
Combinatorics
2024-06-26 v1 Mathematical Physics
Analysis of PDEs
math.MP
Probability
Spectral Theory
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.
Cite
@article{arxiv.2406.17344,
title = {Recurrence and transience for non-Archimedean and directed graphs},
author = {Matthias Keller and Anna Muranova},
journal= {arXiv preprint arXiv:2406.17344},
year = {2024}
}
Comments
21 pages, 5 figures