Asymptotics of the Number of Endpoints of a Random Walk on a Certain Class of Directed Metric Graphs

TL;DR

This paper investigates the long-term behavior of random walks on a specific class of directed metric graphs, deriving asymptotic formulas for the number of possible endpoints as time progresses.

Contribution

It provides new asymptotic results for endpoint counts of random walks on a particular class of directed metric graphs.

Findings

Asymptotic formulas for endpoint counts at large times

Characterization of endpoint distribution behavior

Extension of random walk theory to directed metric graphs

Abstract

A certain class of directed metric graphs is considered. Asymptotics for a number of possible endpoints of a random walk at large times is found.