A note on the Martin boundary of the simple random walk on an example of directed graph

2012/03/15 by Basile de Loynes, de Loynes, Basile
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1203.3314

arxiv created 2012/03/15 · openalex publication_date 2012/03/15 · arxiv updated 2012/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we study the Martin boundary of the simple random walk on an example of directed graph. More precisely, the Martin boundary is shown to be trivial, i.e. there is no non-constant positive harmonic functions. The proof involves fine estimates of the Green function which are summarized in this note.

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