Tilings and discrete Dirichlet problems

DOI10.1007/BF02780322zbMath0938.60070MaRDI QIDQ1264274

Richard W. Kenyon

Publication date: 8 June 2000

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

trapezoidMarkov chainsharmonic function

Mathematics Subject Classification ID

Continuous-time Markov processes on discrete state spaces (60J27)

Related Items

Conformal invariance of planar loop-erased random walks and uniform spanning trees., Boundary value problems on planar graphs and flat surfaces with integer cone singularities, I: The Dirichlet problem, Families of convex tilings, Torus square tilings, Tiling by rectangles and alternating current, The triple intersection property, three dimensional extremal length, and tiling of a topological cube, A “regular” pentagonal tiling of the plane, Boundary value problems on planar graphs and flat surfaces with integer cone singularities. II: The mixed Dirichlet-Neumann problem, Dissections of trapezoids into trapezoids homothetical to trapezoids in a given family, Dimers, tilings and trees, Laplace and bi-Laplace equations for directed networks and Markov chains, Discrete one-forms on meshes and applications to 3D mesh parameterization, A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions, The boundary of a square tiling of a graph coincides with the Poisson boundary

Cites Work

• Planar electric networks. I
• Tilings of convex polygons
• Planar electric networks. II
• Random walks and harmonic functions on infinite planar graphs using square tilings
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