5 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…
Quasi-invariance for SLE welding measures
Shuo Fan, Jinwoo Sung
A large class of Jordan curves on the Riemann sphere can be encoded by circle homeomorphisms via conformal welding, among which we consider the welding homeomorphism of the random…
Area measures and branched polymers in supercritical Liouville quantum gravity
Manan Bhatia, Ewain Gwynne, Jinwoo Sung
We study Liouville quantum gravity (LQG) in the supercritical (a.k.a. strongly coupled) phase, which has background charge and central charge $\mathbf{c}_{\mathrm{L}}…
Quasiconformal deformation of the chordal Loewner driving function and first variation of the Loewner energy
Jinwoo Sung, Yilin Wang
We derive the variational formula of the Loewner driving function of a simple chord under infinitesimal quasiconformal deformations with Beltrami coefficients supported away from t…
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…