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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Advances in Applied Probability
School of Mathematics and Statistics

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