Classification of half-planar maps

• Angel, Omer ^[1] ; Ray, Gourab ^[2]
  1. [1] University of British Columbia

     University of British Columbia

     Canadá

     
  2. [2] University of Cambridge

     University of Cambridge

     Cambridge District, Reino Unido

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 3, 2015, págs. 1315-1349
• Idioma: inglés
• DOI: 10.1214/13-AOP891
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• Resumen

  • 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(p)α. 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.