非阿基米德图和有向图的递归性和暂态性

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-09-18 DOI:10.1002/mana.70040

Matthias Keller, Anna Muranova

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引用次数: 0

摘要

引入了非阿基米德有序域上图的递归和暂态概念。为了实现这一点，我们在这些图和实数上的有向图上的随机游走之间建立了联系。特别地，我们给出了可以用这种方式产生的实有向图的一个表征。作为主要结果，我们给出了递归性和暂态性在容量相关量方面的表征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Recurrence and transience for non-Archimedean and directed graphs

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Recurrence and transience for non-Archimedean and directed graphs

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.

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index