Ewain Gwynne

activity

20112026

most citedThe fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds

73 citations · 304 across the 61 of their papers we have counts for

collaborators

79 papers

math.PR2026

Directed distances in spanning-tree-decorated planar maps: exact exponent, scaling limit and universality

Jacopo Borga, Ewain Gwynne, Yuanzheng Wang

We define a natural orientation on a spanning-tree-decorated planar map whereby, roughly speaking, each directed edge in the map is oriented to match the direction of the contour e…

math.PR2026

Dimension lower bounds in random geometry via Lipschitz functions

Manan Bhatia, Ewain Gwynne, Brin Harper

We prove lower bounds for the Hausdorff dimensions of various natural sets associated with the Liouville quantum gravity (LQG) metric. We prove that the set of 3-star points (i.e.,…

math.PR2026

CaTherine wheels from trees and Liouville quantum gravity

Danny Calegari, Ewain Gwynne

A CaTherine wheel is a space-filling curve $f : S^{1} \to S^{2}$ such that for every closed interval $J \subset S^{1}$ , $f (J)$ is homeomorphic to a closed disk and $f (\partial J)$ is conta…

math.PR2025

Directed distances in bipolar-oriented triangulations: exact exponents and scaling limits

Jacopo Borga, Ewain Gwynne

We study longest and shortest directed paths in the following natural model of directed random planar maps: the uniform infinite bipolar-oriented triangulation (UIBOT), which is th…

math.PR2025

Random walk reflected off of infinity, with applications to uniform spanning forests and supercritical Liouville quantum gravity

Ewain Gwynne, Jinwoo Sung

Let $G$ be an infinite graph -- not necessarily one-ended -- on which the simple random walk is transient. We define a variant of the continuous-time random walk on $\math…

math.PR2025

Liouville Brownian motion and quantum cones in dimension $d > 2$

Federico Bertacco, Ewain Gwynne

For $d > 2$ and $γ \in (0, 2 d)$ , we study the Liouville Brownian motion associated with the whole-space log-correlated Gaussian field in $R^{d}$ . We compute its spectr…

math.PR2024

Inverting the operation of conditioning a branching process on extinction

Ewain Gwynne, Jiaqi Liu

It is well-known that conditioning a supercritical (multi-type) branching process on the event that it eventually becomes extinct yields a subcritical branching process. We study t…

math.DG2024

Approximation of length metrics by conformally flat Riemannian metrics

Andres A. Contreras Hip, Ewain Gwynne

We present a proof of the folklore result that any length metric on $R^{d}$ can be approximated by conformally flat Riemannian distance functions in the uniform distance. Thi…

math.PR2024

Percolation of thick points of the log-correlated Gaussian field in high dimensions

Jian Ding, Ewain Gwynne, Zijie Zhuang

We prove that the set of thick points of the log-correlated Gaussian field contains an unbounded path in sufficiently high dimensions. This contrasts with the two-dimensional case,…

math.PR2024

Area measures and branched polymers in supercritical Liouville quantum gravity

Manan Bhatia, Ewain Gwynne, Jinwoo Sung

We study Liouville quantum gravity (LQG) in the supercritical (a.k.a. strongly coupled) phase, which has background charge $Q \in (0, 2)$ and central charge $\mathbf{c}_{\mathrm{L}}…

math.PR2024

Reconstructing SLE-decorated Liouville quantum gravity surfaces from random permutons

Jacopo Borga, Ewain Gwynne

Permutons constructed from a Liouville quantum gravity surface and a pair of space-filling Schramm-Loewner evolutions (SLEs) have been shown -- or are conjectured -- to describe th…

math.PR2024

Gaussian curvature on random planar maps and Liouville quantum gravity

Andres Contreras Hip, Ewain Gwynne

We investigate the notion of curvature in the context of Liouville quantum gravity (LQG) surfaces. We define the Gaussian curvature for LQG, which we conjecture is the scaling limi…

math.PR2024

Random walk on sphere packings and Delaunay triangulations in arbitrary dimension

Ahmed Bou-Rabee, Ewain Gwynne

We prove that random walks on a family of tilings of d-dimensional Euclidean space, with a canonical choice of conductances, converge to Brownian motion modulo time parameterizatio…

math.PR2023

Cutting $γ$ -Liouville quantum gravity by Schramm-Loewner evolution for $κ \neq \in {γ^{2}, 16/ γ^{2}}$

Morris Ang, Ewain Gwynne

There are many deep and useful theorems relating Schramm-Loewner evolution (SLE $_{κ}$ ) and Liouville quantum gravity ( $γ$ -LQG) in the case when the parameters satisfy $κ\in \{γ^2, 16…

math.PR2023

Tightness of exponential metrics for log-correlated Gaussian fields in arbitrary dimension

Jian Ding, Ewain Gwynne, Zijie Zhuang

We prove the tightness of a natural approximation scheme for an analog of the Liouville quantum gravity metric on $R^{d}$ for arbitrary $d \geq 2$ . More precisely, let $\{h_n\…

math.PR2023

Critical Liouville quantum gravity and CLE $_{4}$

Morris Ang, Ewain Gwynne

Consider a critical ( $γ = 2$ ) Liouville quantum gravity (LQG) disk together with an independent conformal loop ensemble (CLE) with parameter $κ = 4$ . We show that the critical LQG surf…

math.PR2023

Supercritical Liouville quantum gravity and CLE $_{4}$

Morris Ang, Ewain Gwynne

We establish the first relationship between Schramm-Loewner evolution (SLE) and Liouville quantum gravity (LQG) in the supercritical (a.k.a. strongly coupled) phase, which correspo…

math.PR2023

Scaling limits of planar maps under the Smith embedding

Federico Bertacco, Ewain Gwynne, Scott Sheffield

The Smith embedding of a finite planar map with two marked vertices, possibly with conductances on the edges, is a way of representing the map as a tiling of a finite cylinder by r…

math.PR2023

A support theorem for exponential metrics of log-correlated Gaussian fields in arbitrary dimension

Andres A. Contreras Hip, Ewain Gwynne

Let $h$ be a log-correlated Gaussian field on $R^{d}$ , let $γ \in (0, 2 d),$ let $μ_{h}$ be the $γ$ -Gaussian multiplicative chaos measure, and let $D_{h}$ be an exponential metric a…

math.PR2023★ 1 cited

Power-law bounds for increasing subsequences in Brownian separable permutons and homogeneous sets in Brownian cographons

Jacopo Borga, William Da Silva, Ewain Gwynne

The Brownian separable permutons are a one-parameter family -- indexed by $p \in (0, 1)$ -- of universal limits of random constrained permutations. We show that for each $p \in (0, 1)$ ,…

math.PR2022

On the geometry of uniform meandric systems

Jacopo Borga, Ewain Gwynne, Minjae Park

A meandric system of size $n$ is the set of loops formed from two arc diagrams (non-crossing perfect matchings) on ${1, \dots, 2 n}$ , one drawn above the real line and the other bel…

math.PR2022

Internal DLA on mated-CRT maps

Ahmed Bou-Rabee, Ewain Gwynne

We prove a shape theorem for internal diffusion limited aggregation on mated-CRT maps, a family of random planar maps which approximate Liouville quantum gravity (LQG) surfaces. Th…

math.PR2022

The Minkowski content measure for the Liouville quantum gravity metric

Ewain Gwynne, Jinwoo Sung

A Liouville quantum gravity (LQG) surface is a natural random two-dimensional surface, initially formulated as a random measure space and later as a random metric space. We show th…

math.PR2022★ 2 cited

Harmonic balls in Liouville quantum gravity

Ahmed Bou-Rabee, Ewain Gwynne

Harmonic balls are domains which satisfy the mean-value property for harmonic functions. We establish the existence and uniqueness of harmonic balls on Liouville quantum gravity (L…

Directed distances in spanning-tree-decorated planar maps: exact exponent, scaling limit and universality

Dimension lower bounds in random geometry via Lipschitz functions

CaTherine wheels from trees and Liouville quantum gravity

Directed distances in bipolar-oriented triangulations: exact exponents and scaling limits

Random walk reflected off of infinity, with applications to uniform spanning forests and supercritical Liouville quantum gravity

Liouville Brownian motion and quantum cones in dimension d>2

Inverting the operation of conditioning a branching process on extinction

Approximation of length metrics by conformally flat Riemannian metrics

Percolation of thick points of the log-correlated Gaussian field in high dimensions

Area measures and branched polymers in supercritical Liouville quantum gravity

Reconstructing SLE-decorated Liouville quantum gravity surfaces from random permutons

Gaussian curvature on random planar maps and Liouville quantum gravity

Random walk on sphere packings and Delaunay triangulations in arbitrary dimension

Cutting γ-Liouville quantum gravity by Schramm-Loewner evolution for κ∈{γ2,16/γ2}

Tightness of exponential metrics for log-correlated Gaussian fields in arbitrary dimension

Critical Liouville quantum gravity and CLE4​

Supercritical Liouville quantum gravity and CLE4​

Scaling limits of planar maps under the Smith embedding

A support theorem for exponential metrics of log-correlated Gaussian fields in arbitrary dimension

Power-law bounds for increasing subsequences in Brownian separable permutons and homogeneous sets in Brownian cographons

On the geometry of uniform meandric systems

Internal DLA on mated-CRT maps

The Minkowski content measure for the Liouville quantum gravity metric

Harmonic balls in Liouville quantum gravity

Liouville Brownian motion and quantum cones in dimension $d > 2$

Cutting $γ$ -Liouville quantum gravity by Schramm-Loewner evolution for $κ \neq \in {γ^{2}, 16/ γ^{2}}$

Critical Liouville quantum gravity and CLE $_{4}$

Supercritical Liouville quantum gravity and CLE $_{4}$