Recurrence and transience of the edge graph of a tiling of the Euclidean plane

DOI10.1007/BF01446917zbMath0679.60072MaRDI QIDQ1822842

Paolo M. Soardi

Publication date: 1990

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164709

zbMATH Keywords

strong isoperimetric inequalityrecurrentrandom walk on the edge graph of a quasi normal tiling of the plane

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50)

Related Items

Light structures in infinite planar graphs without the strong isoperimetric property, Hyperbolic and parabolic packings, Strong isoperimetric inequalities and combinatorial curvatures on multiply connected planar graphs, On the norms of the random walks on planar graphs, Curvature, geometry and spectral properties of planar graphs, Classification of infinite networks and its application, Rough Isometries and Dirichlet Finite Harmonic Functions on Graphs, Duality properties of strong isoperimetric inequalities on a planar graph and combinatorial curvatures, Geodesics in non-positively curved plane tessellations, Combinatorial modulus and type of graphs, Strong isoperimetric inequality for the edge graph of a tiling of the plane, Circle boundaries of planar graphs, Morphisms and currents in infinite nonlinear resistive networks, Dirichlet norms, capacities and generalized isoperimetric inequalities for Markov operators.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Boundary limit of discrete Dirichlet potentials
• Isoperimetric inequalities and Markov chains
• Tilings whose members have finitely many neighbors
• Random walks on graphs with a strong isoperimetric property
• Uniqueness of currents in infinite resistive networks
• A simple criterion for transience of a reversible Markov chain
• IInfinite Graphs with Nonconstant Dirichlet Finite Harmonic Functions
• Difference Equations, Isoperimetric Inequality and Transience of Certain Random Walks