无重边四边形剖分中的距离统计与minbus的几何
Distance statistics in quadrangulations with no multiple edges and the geometry of minbus
摘要：
我们提出了一个详细的计算距离相关的两点函数的四边形没有多个边缘。在大地图的限制下，计算和分析了测量这两点函数的各种离散观测量。对于大的距离和在缩放制度，我们恢复相同的通用缩放功能一般四边形。然后，我们探讨的几何形状的“最小的脖子婴儿宇宙”（minbus），这是副产品被删除从一般四边形，将其转换成四边形，没有多个边缘，“母亲宇宙”。我们给出了minbus的一些依赖于距离的特征，例如minbus内部的两点函数或从随机点到母宇宙的距离定律。
英文摘要：
We present a detailed calculation of the distance-dependent two-point function for quadrangulations with no multiple edges. Various discrete observables measuring this two-point function are computed and analyzed in the limit of large maps. For large distances and in the scaling regime, we recover the same universal scaling function as for general quadrangulations. We then explore the geometry of "minimal neck baby universes" (minbus), which are the outgrowths to be removed from a general quadrangulation to transform it into a quadrangulation with no multiple edges, the "mother universe". We give a number of distance-dependent characterizations of minbus, such as the two-point function inside a minbu or the law for the distance from a random point to the mother universe.
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