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2014 The scaling limit of uniform random plane maps, via the Ambjørn–Budd bijection
Jérémie Bettinelli, Emmanuel Jacob, Grégory Miermont
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Electron. J. Probab. 19: 1-16 (2014). DOI: 10.1214/EJP.v19-3213

Abstract

We prove that a uniform rooted plane map with n edges converges in distribution after asuitable normalization to the Brownian map for the Gromov–Hausdorff topology. A recent bijection due to Ambjørn and Budd allows to derive this result by a direct coupling with a uniform random quadrangulation with n faces.

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Jérémie Bettinelli. Emmanuel Jacob. Grégory Miermont. "The scaling limit of uniform random plane maps, via the Ambjørn–Budd bijection." Electron. J. Probab. 19 1 - 16, 2014. https://doi.org/10.1214/EJP.v19-3213

Information

Accepted: 19 August 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1320.60088
MathSciNet: MR3256874
Digital Object Identifier: 10.1214/EJP.v19-3213

Subjects:
Primary: 60F17
Secondary: 60C05 , 60D05

Keywords: Bijections , Brownian map , Gromov-Hausdorff topology , Random maps , Random metric spaces , scaling limits

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