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    Geodesics and Bounded Harmonic Functions on Infinite Graphs

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    Date
    1991
    Author
    Northshield, Sam
    Metadata
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    Subject
    Random walk
    planar graphs
    geodesic rays
    harmonic functions
    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.
    Description
    This article has been published in the September 1991 issue of Proceedings of the American Mathematical Society.
    URI
    http://hdl.handle.net/1951/69950
    Collections
    • Mathematics Faculty Work [20]

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