Random walk on a directed graph and Martin boundary
Basile de Loynes
TL;DR
This paper investigates the Martin boundary for a simple random walk on a partially oriented lattice, demonstrating its triviality through detailed Green kernel estimates.
Contribution
It provides a novel analysis of the Martin boundary for directed graphs, specifically showing triviality in a new lattice example.
Findings
Martin boundary is trivial for the studied lattice
Green kernel estimates are crucial for the analysis
Advances understanding of boundary behavior in directed graphs
Abstract
The Martin boundary associated with the simple random walk on an example of partially oriented lattice is shown to be trivial by computing fine estimates of the Green kernel.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Mathematical Dynamics and Fractals · Theoretical and Computational Physics