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

Showing 2019Show all

14 papers · 1 filter

math.PR2019★ 45 cited

Mating of trees for random planar maps and Liouville quantum gravity: a survey

Ewain Gwynne, Nina Holden, Xin Sun

We survey the theory and applications of mating-of-trees bijections for random planar maps and their continuum analog: the mating-of-trees theorem of Duplantier, Miller, and Sheffi…

math.PR2019★ 11 cited

The dimension of the boundary of a Liouville quantum gravity metric ball

Ewain Gwynne

Let $γ \in (0, 2)$ , let $h$ be the planar Gaussian free field, and consider the $γ$ -Liouville quantum gravity (LQG) metric associated with $h$ . We show that the essential supremum of…

math.PR2019

Random surfaces and Liouville quantum gravity

Ewain Gwynne

Liouville quantum gravity (LQG) surfaces are a family of random fractal surfaces which can be thought of as the canonical models of random two-dimensional Riemannian manifolds, in…

math.PR2019

KPZ formulas for the Liouville quantum gravity metric

Ewain Gwynne, Joshua Pfeffer

Let $γ \in (0, 2)$ , let $h$ be the planar Gaussian free field, and let $D_{h}$ be the associated $γ$ -Liouville quantum gravity (LQG) metric. We prove that for any random Borel set $X \…

math.PR2019

Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense

Ewain Gwynne, Nina Holden, Xin Sun

Recent works have shown that random triangulations decorated by critical ( $p = 1/2$ ) Bernoulli site percolation converge in the scaling limit to a $8/3$ -Liouville quantum grav…

math.PR2019★ 3 cited

Conformal covariance of the Liouville quantum gravity metric for $γ \in (0, 2)$

Ewain Gwynne, Jason Miller

For $γ \in (0, 2)$ , $U \subset C$ , and an instance $h$ of the Gaussian free field (GFF) on $U$ , the $γ$ -Liouville quantum gravity (LQG) surface associated with $(U, h)$ is form…

math.PR2019★ 4 cited

Existence and uniqueness of the Liouville quantum gravity metric for $γ \in (0, 2)$

Ewain Gwynne, Jason Miller

We show that for each $γ \in (0, 2)$ , there is a unique metric (i.e., distance function) associated with $γ$ -Liouville quantum gravity (LQG). More precisely, we show that for the who…

math.PR2019

Confluence of geodesics in Liouville quantum gravity for $γ \in (0, 2)$

Ewain Gwynne, Jason Miller

We prove that for any metric which one can associate with a Liouville quantum gravity (LQG) surface for $γ \in (0, 2)$ satisfying certain natural axioms, its geodesics exhibit the fo…

math.PR2019

Weak LQG metrics and Liouville first passage percolation

Julien Dubédat, Hugo Falconet, Ewain Gwynne +2

For $γ \in (0, 2)$ , we define a weak $γ$ -Liouville quantum gravity (LQG) metric to be a function $h \mapsto D_{h}$ which takes in an instance of the planar Gaussian free field (GFF) and…

math.PR2019

Local metrics of the Gaussian free field

Ewain Gwynne, Jason Miller

We introduce the concept of a local metric of the Gaussian free field (GFF) $h$ , which is a random metric coupled with $h$ in such a way that it depends locally on $h$ in a certain…

math.PR2019

Bounds for distances and geodesic dimension in Liouville first passage percolation

Ewain Gwynne, Joshua Pfeffer

For $ξ \geq 0$ , Liouville first passage percolation (LFPP) is the random metric on $ε Z^{2}$ obtained by weighting each vertex by $ε e^{ξ h_{ε} (z)}$ …

math.PR2019★ 5 cited

Liouville quantum gravity surfaces with boundary as matings of trees

Morris Ang, Ewain Gwynne

For $γ \in (0, 2)$ , the quantum disk and $γ$ -quantum wedge are two of the most natural types of Liouville quantum gravity (LQG) surfaces with boundary. These surfaces arise as scalin…

math.PR2019★ 16 cited

Liouville quantum gravity with matter central charge in $(1, 25)$ : a probabilistic approach

Ewain Gwynne, Nina Holden, Joshua Pfeffer +1

There is a substantial literature concerning Liouville quantum gravity (LQG) in two dimensions with conformal matter field of central charge ${\mathbf{c}}_{\mathrm M}\in(-\infty,1]…

math.PR2019

External diffusion limited aggregation on a spanning-tree-weighted random planar map

Ewain Gwynne, Joshua Pfeffer

Let $M$ be the infinite spanning-tree-weighted random planar map, which is the local limit of finite random planar maps sampled with probability proportional to the number of spann…

Mating of trees for random planar maps and Liouville quantum gravity: a survey

The dimension of the boundary of a Liouville quantum gravity metric ball

Random surfaces and Liouville quantum gravity

KPZ formulas for the Liouville quantum gravity metric

Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense

Conformal covariance of the Liouville quantum gravity metric for γ∈(0,2)

Existence and uniqueness of the Liouville quantum gravity metric for γ∈(0,2)

Confluence of geodesics in Liouville quantum gravity for γ∈(0,2)

Weak LQG metrics and Liouville first passage percolation

Local metrics of the Gaussian free field

Bounds for distances and geodesic dimension in Liouville first passage percolation

Liouville quantum gravity surfaces with boundary as matings of trees

Liouville quantum gravity with matter central charge in (1,25): a probabilistic approach

External diffusion limited aggregation on a spanning-tree-weighted random planar map

Conformal covariance of the Liouville quantum gravity metric for $γ \in (0, 2)$

Existence and uniqueness of the Liouville quantum gravity metric for $γ \in (0, 2)$

Confluence of geodesics in Liouville quantum gravity for $γ \in (0, 2)$

Liouville quantum gravity with matter central charge in $(1, 25)$ : a probabilistic approach