CLASSIFICATION OF HALF-PLANAR MAPS
成果类型：
Article
署名作者：
Angel, Omer; Ray, Gourab
署名单位：
University of British Columbia; University of Cambridge
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/13-AOP891
发表日期：
2015
页码：
1315-1349
关键词：
摘要：
We characterize all translation invariant half-planar maps satisfying a certain natural domain Markov property. For p-angulations with p >= 3 where all faces are simple, we show that these form a one-parameter family of measures H-alpha((p)). 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 subcritical maps are identified as all possible limits of uniform measures on finite maps with given boundary and area.
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