Random walk with barriers on a graph

TL;DR

This paper analyzes an asymmetric discrete random walk on a graph with multiple barriers, deriving key metrics like expected arrivals, absorption probabilities, and absorption times considering specific edge and vertex probabilities.

Contribution

It introduces a method to compute absorption-related metrics for asymmetric random walks on graphs with multiple barriers, incorporating vertex and edge-specific probabilities.

Findings

Derived formulas for expected number of arrivals

Calculated absorption probabilities at barriers

Determined expected time until absorption

Abstract

We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex (barrier) specific probabilities are defined.