73 citations · 304 across the 61 of their papers we have counts for
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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…
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 can be approximated by conformally flat Riemannian distance functions in the uniform distance. Thi…
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,…
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 and central charge $\mathbf{c}_{\mathrm{L}}…
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…
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…
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…