Geodesics and bounded harmonic functions on infinite planar graphs
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- by S. Northshield PDF
- Proc. Amer. Math. Soc. 113 (1991), 229-233 Request permission
Abstract:
It is shown there that an infinite connected planar graph with a uniform upper bound on vertex degree and rapidly decreasing Green’s function (relative to the simple random walk) has infinitely many pairwise finitely-intersecting geodesic rays starting at each vertex. We then demonstrate the existence of nonconstant bounded harmonic functions on the graph.References
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- Wilfrid S. Kendall, Brownian motion on a surface of negative curvature, Seminar on probability, XVIII, Lecture Notes in Math., vol. 1059, Springer, Berlin, 1984, pp. 70–76. MR 770949, DOI 10.1007/BFb0100032 S. Northshield, Schrödinger operators on infinite graphs, doctoral dissertation, Univ. of Rochester, 1989.
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 229-233
- MSC: Primary 60J15
- DOI: https://doi.org/10.1090/S0002-9939-1991-1076576-5
- MathSciNet review: 1076576