Classification of Half Planar Maps
Classification of Half Planar Maps
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半平面地图的分类
DOI：
10.1214/13-aop891
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
G. Ray
中科院分区：
文献类型：
--
作者：
Omer Angel;G. Ray
我们刻画了所有平移不变的半平面映射满足一定的自然域马尔可夫性质。对于p \ge 3的p-角化，其中所有的面都是简单的，我们证明了这些形成了一个单参数测度族H^{（p）}_{alpha}。对于三角剖分，我们还建立了一个相变的存在，影响这些地图的许多属性。临界映射是著名的半平面一致无限平面映射。次临界映射被定义为具有给定边界和面积的有限映射上一致测度的所有可能极限。
We characterize all translation invariant half planar maps satisfying a certain natural domain Markov property. For p-angulations with p \ge 3 where all faces are simple, we show that these form a one-parameter family of measures H^{(p)}_{alpha}. For triangulations we also establish existence of a phase transition which affects many properties of these maps. The critical maps are the well known half plane uniform infinite planar maps. The sub-critical maps are identified as all possible limits of uniform measures on finite maps with given boundary and area.