The Scaling Limit of Random Outerplanar Maps

2014/05/08 by Alessandra Caraceni, Caraceni, Alessandra
Mathematics · #60C05 #60F05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60C05 #msc:60F05

paper · pdf · doi:10.48550/arxiv.1405.1971

25 pages

arxiv created 2014/05/08 · arxiv updated 2014/05/09

Abstract

A planar map is outerplanar if all its vertices belong to the same face. We show that random uniform outerplanar maps with n vertices suitably rescaled by a factor 1/ √(n) converge in the Gromov-Hausdorff sense to (7 √(2))/(9) times Aldous' Brownian tree. The proof uses the bijection of Bonichon, Gavoille and Hanusse.

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