arXiv Open Access 2015

Bipolar orientations on planar maps and SLE$_{12}$

Richard Kenyon Jason Miller Scott Sheffield David B. Wilson

Lihat Sumber

Abstrak

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 $\sqrt{4/3}$-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.

Topik & Kata Kunci

math.PR math-ph math.CV

Penulis (4)

Richard Kenyon

Jason Miller

Scott Sheffield

David B. Wilson

Format Sitasi

APA MLA BibTeX

Kenyon, R., Miller, J., Sheffield, S., Wilson, D.B. (2015). Bipolar orientations on planar maps and SLE$_{12}$. https://arxiv.org/abs/1511.04068

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2015
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓