73 citations · 304 across the 61 of their papers we have counts for
7 papers · 1 filter
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…
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…
Anomalous diffusion of random walk on random planar maps
Ewain Gwynne, Tom Hutchcroft
We prove that the simple random walk on the uniform infinite planar triangulation (UIPT) typically travels graph distance at most in units of time. Together…
The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds
Jian Ding, Ewain Gwynne
We prove that for each , there is an exponent , the "fractal dimension of -Liouville quantum gravity (LQG)", which describes the ball volume growth exponent…
Connectivity properties of the adjacency graph of SLE bubbles for
Ewain Gwynne, Joshua Pfeffer
We study the adjacency graph of bubbles---i.e., complementary connected components---of an SLE curve for , with two such bubbles considered to be adjacent if their…