Geodesics in Large Planar Maps and in the Brownian Map
نویسنده
چکیده
We study geodesics in the random metric space called the Brownian map, which appears as the scaling limit of large planar maps. In particular, we completely describe geodesics starting from the distinguished point called the root, and we characterize the set of all points that are connected to the root by more than one geodesic. We also prove that points of the Brownian map can be connected to the root by at most three distinct geodesics. Our results have applications to the behavior of geodesics in large planar maps.
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تاریخ انتشار 2008