107 citations · 484 across the 43 of their papers we have counts for
6 papers · 1 filter
The geodesics in Liouville quantum gravity are not Schramm-Loewner evolutions
Jason Miller, Wei Qian
We prove that the geodesics associated with any metric generated from Liouville quantum gravity (LQG) which satisfies certain natural hypotheses are necessarily singular with respe…
Conformal invariance of CLE on the Riemann sphere for
Ewain Gwynne, Jason Miller, Wei Qian
The conformal loop ensemble (CLE) is the canonical conformally invariant probability measure on non-crossing loops in a simply connected domain in and is indexed by a p…
Uniqueness of the welding problem for SLE and Liouville quantum gravity
Oliver McEnteggart, Jason Miller, Wei Qian
We give a simple set of geometric conditions on curves , in from to so that if is a homeomorphism whic…
The Tutte embedding of the Poisson-Voronoi tessellation of the Brownian disk converges to -Liouville quantum gravity
Ewain Gwynne, Jason Miller, Scott Sheffield
Recent works have shown that an instance of a Brownian surface (such as the Brownian map or Brownian disk) a.s. has a canonical conformal structure under which it is equivalent to…
An invariance principle for ergodic scale-free random environments
Ewain Gwynne, Jason Miller, Scott Sheffield
There are many classical random walk in random environment results that apply to ergodic random planar environments. We extend some of these results to random environments in which…
Harmonic functions on mated-CRT maps
Ewain Gwynne, Jason Miller, Scott Sheffield
A mated-CRT map is a random planar map obtained as a discretized mating of correlated continuum random trees. Mated-CRT maps provide a coarse-grained approximation of many other na…