73 citations · 304 across the 61 of their papers we have counts for
6 papers · 1 filter
On the geometry of uniform meandric systems
Jacopo Borga, Ewain Gwynne, Minjae Park
A meandric system of size is the set of loops formed from two arc diagrams (non-crossing perfect matchings) on , one drawn above the real line and the other bel…
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…
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…
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…
Permutons, meanders, and SLE-decorated Liouville quantum gravity
Jacopo Borga, Ewain Gwynne, Xin Sun
We study a class of random permutons which can be constructed from a pair of space-filling Schramm-Loewner evolution (SLE) curves on a Liouville quantum gravity (LQG) surface. This…
Loewner evolution driven by complex Brownian motion (with simulations by Minjae Park)
Ewain Gwynne, Joshua Pfeffer
We study the Loewner evolution whose driving function is , where is a pair of Brownian motions with a given covariance matrix. This model can be…