Quadrangulations with no pendant vertices (Q373522)
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scientific article; zbMATH DE number 6216072
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quadrangulations with no pendant vertices |
scientific article; zbMATH DE number 6216072 |
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Quadrangulations with no pendant vertices (English)
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17 October 2013
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A quadrangulation is a planar map with four vertices incident to any face. Pendant vertices (with degree 1) are not allowed. A random quadrangulation is assumed to be uniformly distributed over the set of all rooted quadrangulations with \(n\) faces. Using a bijection between planar maps and certain labeled trees, it is shown that there holds a convergence in distribution to a Brownian map for \(n\) tending towards infinity.
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random planar maps
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Brownian map
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Schaeffer's bijection
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Gromov-Hausdorff convergence
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