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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…
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…
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…
Liouville Brownian motion and quantum cones in dimension
Federico Bertacco, Ewain Gwynne
For and , we study the Liouville Brownian motion associated with the whole-space log-correlated Gaussian field in . We compute its spectr…
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…