107 citations · 484 across the 43 of their papers we have counts for
11 papers · 1 filter
Non-simple SLE curves are not determined by their range
Jason Miller, Scott Sheffield, Wendelin Werner
We show that when observing the range of a chordal SLE curve for , it is not possible to recover the order in which the points have been visited. We also derive rel…
Liouville quantum gravity and the Brownian map III: the conformal structure is determined
Jason Miller, Scott Sheffield
Previous works in this series have shown that an instance of a -Liouville quantum gravity (LQG) sphere has a well-defined distance function, and that the resulting metr…
Convergence of the self-avoiding walk on random quadrangulations to SLE on -Liouville quantum gravity
Ewain Gwynne, Jason Miller
We prove that a uniform infinite quadrangulation of the half-plane decorated by a self-avoiding walk (SAW) converges in the scaling limit to the metric gluing of two independent Br…
Metric gluing of Brownian and -Liouville quantum gravity surfaces
Ewain Gwynne, Jason Miller
In a recent series of works, Miller and Sheffield constructed a metric on -Liouville quantum gravity (LQG) under which -LQG surfaces (e.g., the LQG sphere,…
Scaling limit of the uniform infinite half-plane quadrangulation in the Gromov-Hausdorff-Prokhorov-uniform topology
Ewain Gwynne, Jason Miller
We prove that the uniform infinite half-plane quadrangulation (UIHPQ), with either general or simple boundary, equipped with its graph distance, its natural area measure, and the c…
Gaussian free field light cones and SLE
Jason Miller, Scott Sheffield
We derive a surprising correspondence between SLE processes and light cones of the Gaussian free field (GFF). Recall that (one-sided, chordal, origin-seeded) SLE proc…