Markov chains arising from graphs over ordered fields

07.12.2023, 13:00  –  Haus 9, Raum 0.17 und Zoom
Forschungsseminar Diskrete Spektraltheorie

Anna Muranova (University of Warmia and Mazury in Olsztyn)

Abstract: In this talk we consider graphs, whose weights belong to an ordered field. It is known, that in the case of real weights every weighted graph defines a Markov chain, whose states are vertices of the graph. Moreover, a type of state (recurrent or transient)  in the Markov chain is closely related to a capacity of the vertex. We show, how the corresponding Markov chain can be defined  in case of graphs with weight from non-Archimedean ordered field. Then we discuss the possibilities to relate a type of state in the Markov chain with the non-Archimedean capacity of the vertex in the graph.