Browsing Mathematics Faculty Work by Subject "geodesic rays"
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Geodesics and Bounded Harmonic Functions on Infinite GraphsIt 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.
