12 papers
Random walk reflected off of infinity, with applications to uniform spanning forests and supercritical Liouville quantum gravity
Ewain Gwynne, Jinwoo Sung
Let be an infinite graph -- not necessarily one-ended -- on which the simple random walk is transient. We define a variant of the continuous-time random walk on $\math…
Dimension lower bounds in random geometry via Lipschitz functions
Manan Bhatia, Ewain Gwynne, Brin Harper
We prove lower bounds for the Hausdorff dimensions of various natural sets associated with the Liouville quantum gravity (LQG) metric. We prove that the set of 3-star points (i.e.,…
CaTherine wheels from trees and Liouville quantum gravity
Danny Calegari, Ewain Gwynne
A CaTherine wheel is a space-filling curve such that for every closed interval , is homeomorphic to a closed disk and is conta…
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,…
Joint scaling limit of a bipolar-oriented triangulation and its dual in the peanosphere sense
Ewain Gwynne, Nina Holden, Xin Sun
Kenyon, Miller, Sheffield, and Wilson (2015) showed how to encode a random bipolar-oriented planar map by means of a random walk with a certain step size distribution. Using this e…
Directed distances in bipolar-oriented triangulations: exact exponents and scaling limits
Jacopo Borga, Ewain Gwynne
We study longest and shortest directed paths in the following natural model of directed random planar maps: the uniform infinite bipolar-oriented triangulation (UIBOT), which is th…