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

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Showing 2023Show all

7 papers · 1 filter

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 $p \in (0, 1)$ ,…

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

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 $_{4}$