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math.PR2026
Directed distances in spanning-tree-decorated planar maps: exact exponent, scaling limit and universality
Jacopo Borga, Ewain Gwynne, Yuanzheng Wang
We define a natural orientation on a spanning-tree-decorated planar map whereby, roughly speaking, each directed edge in the map is oriented to match the direction of the contour e…
math.PR2026
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.,…
math.PR2026
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…