Classification of scaling limits of uniform quadrangulations with a boundary

Baur, Erich; Miermont, Grégory; Ray, Gourab (2019). Classification of scaling limits of uniform quadrangulations with a boundary The Annals of Probability, 47(6), pp. 3397-3477. The Institute of Mathematical Statistics 10.1214/18-AOP1316

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We study noncompact scaling limits of uniform random planar quadrangulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe different limiting metric spaces. Among well-known objects like the Brownian plane or the self-similar continuum random tree, we construct two new one-parameter families of metric spaces that appear as scaling limits: the Brownian half-plane with skewness parameter θ and the infinite-volume Brownian disk of perimeter σ. We also obtain various coupling and limit results clarifying the relation between these objects.

Item Type:	Journal Article (Original Article)
Division/Institute:	School of Engineering and Computer Science > Institut für Optimierung und Datenanalyse IODA School of Engineering and Computer Science
Name:	Baur, Erich; Miermont, Grégory and Ray, Gourab
Subjects:	Q Science > QA Mathematics
ISSN:	0091-1798
Publisher:	The Institute of Mathematical Statistics
Language:	English
Submitter:	Erich Baur
Date Deposited:	09 Dec 2019 15:37
Last Modified:	09 Dec 2019 15:37
Publisher DOI:	10.1214/18-AOP1316
Related URLs:	Publication
ArXiv ID:	arXiv:1608.01129
Uncontrolled Keywords:	Planar map, quadrangulation, Brownian map, Brownian disk, Brownian tree, scaling limit, Gromov–Hausdorff convergence
ARBOR DOI:	10.24451/arbor.9326
URI:	https://arbor.bfh.ch/id/eprint/9326