Bipolar orientations on planar maps and SLE12

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 wit...

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Bibliographic Details
Main Authors: Kenyon, Richard, Miller, Jason, Sheffield, Scott Roger, Wilson, David B.
Other Authors: Massachusetts Institute of Technology. Department of Mathematics
Format: Article
Language:English
Published: Institute of Mathematical Statistics 2020
Online Access:https://hdl.handle.net/1721.1/125760