Bipolar orientations on planar maps and SLE12
Name
1511.04068.pdf
Description
Submitted version
Size
646 KB
Format
Adobe PDF
Checksum (MD5)
fe9e8b5b625a103b5f5bec2b78f3ce8d
Author(s)
Kenyon, Richard
Miller, Jason
Sheffield, Scott Roger
Wilson, David B.
Date Issued
May 2019
Journal
Annals of Probability
Publisher
Institute of Mathematical Statistics
Citation
Kenyon, Richard et al., "Bipolar orientations on planar maps and SLE12." Annals of Probability 47, 3 (May 2019): 1240-1269. ©2019 Institute of Mathematical Statistics.
Version
Original manuscript
Abstract
We give bijections between bipolar-oriented (acyclic with unique source and sink) planar maps and certain random walks, which show that the uniformly random bipolar-oriented planar map, decorated by the "peano curve" surrounding the tree of left-most paths to the sink, converges in law with respect to the peanosphere topology to a √4/3-Liouville quantum gravity surface decorated by an independent Schramm-Loewner evolution with parameter κ = 12 (i.e., SLE 12 ). This result is universal in the sense that it holds for bipolar-oriented triangulations, quadrangulations, k-angulations and maps in which face sizes are mixed. Keywords: Bipolar oriention; random planar map; Schramm–Loewner evolution; Liouville quantum gravity; continuum; random tree
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://dx.doi.org/10.1214/18-aop1282
