73 citations · 304 across the 61 of their papers we have counts for
7 papers · 2 filters
Random walk on random planar maps: spectral dimension, resistance, and displacement
Ewain Gwynne, Jason Miller
We study simple random walk on the class of random planar maps which can be encoded by a two-dimensional random walk with i.i.d. increments or a two-dimensional Brownian motion via…
A mating-of-trees approach for graph distances in random planar maps
Ewain Gwynne, Nina Holden, Xin Sun
We introduce a general technique for proving estimates for certain random planar maps which belong to the -Liouville quantum gravity (LQG) universality class for . T…
The Tutte embedding of the mated-CRT map converges to Liouville quantum gravity
Ewain Gwynne, Jason Miller, Scott Sheffield
We prove that the Tutte embeddings (a.k.a. harmonic/barycentric embeddings) of certain random planar maps converge to -Liouville quantum gravity (-LQG). Specifically, we trea…
Convergence of percolation on uniform quadrangulations with boundary to SLE on -Liouville quantum gravity
Ewain Gwynne, Jason Miller
Let be a free Boltzmann quadrangulation with simple boundary decorated by a critical () face percolation configuration. We prove that the chordal percolation exploration…
Characterizations of SLE for on Liouville quantum gravity
Ewain Gwynne, Jason Miller
We prove that SLE for on an independent -Liouville quantum gravity (LQG) surface is uniquely characterized by the form of its LQG boundary length proce…
Convergence of the free Boltzmann quadrangulation with simple boundary to the Brownian disk
Ewain Gwynne, Jason Miller
We prove that the free Boltzmann quadrangulation with simple boundary and fixed perimeter, equipped with its graph metric, natural area measure, and the path which traces its bound…
Chordal SLE explorations of a quantum disk
Ewain Gwynne, Jason Miller
We consider a particular type of -Liouville quantum gravity surface called a doubly marked quantum disk (equivalently, a Brownian disk) decorated by an independent chor…