Recurrence and transience of the edge graph of a tiling of the Euclidean plane
We prove that the simple random walk on the edge graph of a quasi normal tiling of the plane (a generalization of normal tilings) is recurrent. Moreover we prove a sufficient condition on the degrees of the vertices in order that the edge graph of a (non quasi normal) tiling (with tiles having a fixed number of vertices) satisfies a strong isoperimetric inequality.
random walk on the edge graph of a quasi normal tiling of the plane
scientific article; zbMATH DE number 4113689