均匀无限大半平面四边形剖分中的测地线返回边界
Geodesic rays in the uniform infinite half-planar quadrangulation return to the boundary
摘要：
我们表明，所有的测地线在统一的无限半平面四边形（UIHPQ）相交的边界无限多次，从而回答了最近的问题Curien。然而，可能的交点沿边界稀疏分布。作为中间步骤，我们证明了UIHPQ中的测地线是正确的，这是Caraceni和Curien（2015）最近通过与我们不同的推理建立的事实。最后，我们认为，测地线在均匀无限半平面三角剖分的行为在一个非常相似的方式，甚至在一个很强的定量意义。
英文摘要：
We show that all geodesic rays in the uniform infinite half-planar quadrangulation (UIHPQ) intersect the boundary infinitely many times, answering thereby a recent question of Curien. However, the possible intersection points are sparsely distributed along the boundary. As an intermediate step, we show that geodesic rays in the UIHPQ are proper, a fact that was recently established by Caraceni and Curien (2015) by a reasoning different from ours. Finally, we argue that geodesic rays in the uniform infinite half-planar triangulation behave in a very similar manner, even in a strong quantitative sense.
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