107 citations · 484 across the 43 of their papers we have counts for
8 papers · 1 filter
Liouville quantum gravity as a metric space and a scaling limit
Jason Miller
Over the past few decades, two natural random surface models have emerged within physics and mathematics. The first is Liouville quantum gravity, which has its roots in string theo…
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…
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…
Connection probabilities for conformal loop ensembles
Jason Miller, Wendelin Werner
The goal of the present paper is to explain, based on properties of the conformal loop ensembles CLE (both with simple and non-simple loops, i.e., for the whole range $κ\in (8/…
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…