5 papers · 1 filter
Supercritical Liouville quantum gravity and CLE
Morris Ang, Ewain Gwynne
We establish the first relationship between Schramm-Loewner evolution (SLE) and Liouville quantum gravity (LQG) in the supercritical (a.k.a. strongly coupled) phase, which correspo…
The moduli of annuli in random conformal geometry
Morris Ang, Guillaume Remy, Xin Sun
We obtain exact formulae for three basic quantities in random conformal geometry that depend on the modulus of an annulus. The first is for the law of the modulus of the Brownian a…
Critical Liouville quantum gravity and CLE
Morris Ang, Ewain Gwynne
Consider a critical () Liouville quantum gravity (LQG) disk together with an independent conformal loop ensemble (CLE) with parameter . We show that the critical LQG su…
Quantum triangles and imaginary geometry flow lines
Morris Ang, Xin Sun, Pu Yu
We define a three-parameter family of random surfaces in Liouville quantum gravity (LQG) which can be viewed as the quantum version of triangles. These quantum triangles are natura…
Liouville conformal field theory and the quantum zipper
Morris Ang
Sheffield showed that conformally welding a -Liouville quantum gravity (LQG) surface to itself gives a Schramm-Loewner evolution (SLE) curve with parameter $κ= γ^2$ as the in…