Ewain Gwynne

activity

20182021

most citedUp-to-constants comparison of Liouville first passage percolation and Liouville quantum gravity

1 citations · 1 across the 2 of their papers we have counts for

collaborators

22 papers

math.PR2021

The critical Liouville quantum gravity metric induces the Euclidean topology

Jian Ding, Ewain Gwynne

We show that every possible metric associated with critical ( $γ = 2$ ) Liouville quantum gravity (LQG) induces the same topology on the plane as the Euclidean metric. More precisely,…

math.PR2021★ 1 cited

Up-to-constants comparison of Liouville first passage percolation and Liouville quantum gravity

Jian Ding, Ewain Gwynne

Liouville first passage percolation (LFPP) with parameter $ξ > 0$ is the family of random distance functions ${D_{h}^{ε}}_{ε > 0}$ on the plane obtained by integrating $e^{ξ h_{ε}}$ along…

math.PR2020

Geodesic networks in Liouville quantum gravity surfaces

Ewain Gwynne

Recent work has shown that for $γ \in (0, 2)$ , a Liouville quantum gravity (LQG) surface can be endowed with a canonical metric. We prove several results concerning geodesics for thi…

math.PR2020

Tightness of supercritical Liouville first passage percolation

Jian Ding, Ewain Gwynne

Liouville first passage percolation (LFPP) with parameter $ξ > 0$ is the family of random distance functions ${D_{h}^{ε}}_{ε > 0}$ on the plane obtained by integrating $e^{ξ h_{ε}}$ along p…

math.PR2019

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…