We discuss percolation and random walks in a class of homogeneous ultrametric spaces together with similarities and differences in ultrametric and Euclidean spaces. We briefly outline the role of these models in the study of interacting systems. Several open problems are presented.

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Keywords hierarchical lattice, interacting system, branching, percolation, random graph, random walk, Ultrametric space
Persistent URL dx.doi.org/10.1017/apr.2018.72
Journal Advances in Applied Probability
Dawson, D.A, & Gorostiza, L.G. (L. G.). (2018). Random systems in ultrametric spaces. Advances in Applied Probability, 50(A), 83–97. doi:10.1017/apr.2018.72