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:

Engineering and Information Technology > Institut für Optimierung und Datenanalyse IODA
Engineering and Information Technology

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:

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

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