2003/08/10 by Itai Benjamini, Itaï Benjamini, Benjamini, Itai +2
Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Point processes and geometric inequalities #Stochastic processes and statistical mechanics #math.MG
paper · pdf · doi:10.48550/arxiv.math/0308092
arxiv created 2003/08/10 · openalex publication_date 2003/08/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
ω-periodic graphs are introduced and studied. These are graphs which arise as the limits of periodic extensions of the nearest neighbor graph on the integers. We observe that all bounded degree ω-periodic graphs are ameanable. We also provide examples of ω-periodic graphs which have exponential volume growth, non-linear polynomial volume growth and intermediate volume growth.