374 citations · 1.2k across the 68 of their papers we have counts for
4 papers · 2 filters
Bipolar orientations on planar maps and SLE
Richard Kenyon, Jason Miller, Scott Sheffield +1
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…
Liouville quantum gravity and the Brownian map I: The QLE(8/3,0) metric
Jason Miller, Scott Sheffield
Liouville quantum gravity (LQG) and the Brownian map (TBM) are two distinct models of measure-endowed random surfaces. LQG is defined in terms of a real parameter , and it has l…
An axiomatic characterization of the Brownian map
Jason Miller, Scott Sheffield
The Brownian map is a random sphere-homeomorphic metric measure space obtained by "gluing together" the continuum trees described by the and coordinates of the Brownian sna…
Liouville quantum gravity spheres as matings of finite-diameter trees
Jason Miller, Scott Sheffield
We show that the unit area Liouville quantum gravity sphere can be constructed in two equivalent ways. The first, which was introduced by the authors and Duplantier, uses a Bessel…