The topology of scaling limits of positive genus random quadrangulations
نویسندگان
چکیده
منابع مشابه
The Topology of Scaling Limits of Positive Genus Random Quadrangulations
We discuss scaling limits of large bipartite quadrangulations of positive genus. For a given g, we consider, for every n ≥ 1, a random quadrangulation qn uniformly distributed over the set of all rooted bipartite quadrangulations of genus g with n faces. We view it as a metric space by endowing its set of vertices with the graph distance. As n tends to infinity, this metric space, with distance...
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We discuss scaling limits of large bipartite quadrangulations of positive genus. For a given g, we consider, for every n≥ 1, a random quadrangulation qn uniformly distributed over the set of all rooted bipartite quadrangulations of genus g with n faces. We view it as a metric space by endowing its set of vertices with the graph distance. We show that, as n tends to infinity, this metric space, ...
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We discuss the scaling limit of large planar quadrangulations with a boundary whose length is of order the square root of the number of faces. We consider a sequence (σn) of integers such that σn/ √ 2n tends to some σ ∈ [0,∞]. For every n ≥ 1, we call qn a random map uniformly distributed over the set of all rooted planar quadrangulations with a boundary having n faces and 2σn half-edges on the...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2012
ISSN: 0091-1798
DOI: 10.1214/11-aop675