Publications (25)
Cutting -Liouville quantum gravity by Schramm-Loewner evolution for $κ\not\in \{γ^2, 16/γ^2\}$
Morris Ang, Ewain Gwynne
There are many deep and useful theorems relating Schramm-Loewner evolution (SLE) and Liouville quantum gravity (-LQG) in the case when the parameters satisfy $κ\in \{γ^2…
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…
Conformal welding of quantum disks
Morris Ang, Nina Holden, Xin Sun
Two-pointed quantum disks with a weight parameter are a family of finite-area random surfaces that arise naturally in Liouville quantum gravity. In this paper we show that…
Exact solution of three-point functions in critical loop models
Morris Ang, Gefei Cai, Jesper Lykke Jacobsen +4
We propose an exact formula for three-point functions on the sphere in critical loop models with primary fields characterized by legs and a parameter \(s\) that de…
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…
Quantum Loewner evolution in quantum natural time: phases and Markov properties
Morris Ang, Deven Mithal
Quantum Loewner evolution (QLE)$(γ^2, η)$ is a family of growth processes in random environments, introduced by Miller and Sheffield (arXiv:1312.5745) as candidate scaling limits…
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…
FZZ formula of boundary Liouville CFT via conformal welding
Morris Ang, Guillaume Remy, Xin Sun
Liouville Conformal Field Theory (LCFT) on the disk describes the conformal factor of the quantum disk, which is the natural random surface in Liouville quantum gravity with disk t…
Integrability of Conformal Loop Ensemble: Imaginary DOZZ Formula and Beyond
Morris Ang, Gefei Cai, Xin Sun +1
The scaling limit of the probability that points are on the same cluster for 2D critical percolation is believed to be governed by a conformal field theory (CFT). Although this…
Boundary touching probability and nested-path exponent for non-simple CLE
Morris Ang, Xin Sun, Pu Yu +1
The conformal loop ensemble (CLE) has two phases: for , the loops are simple and do not touch each other or the boundary; for , the loops are non-simpl…
Volume of metric balls in Liouville quantum gravity
Morris Ang, Hugo Falconet, Xin Sun
We study the volume of metric balls in Liouville quantum gravity (LQG). For , it has been known since the early work of Kahane (1985) and Molchan (1996) that the LQG v…
Reversibility of whole-plane SLE for
Morris Ang, Pu Yu
Whole-plane SLE is a random fractal curve between two points on the Riemann sphere. Zhan established for that whole-plane SLE is reversible, meaning invariant…
Large deviations of radial SLE
Morris Ang, Minjae Park, Yilin Wang
We derive the large deviation principle for radial Schramm-Loewner evolution () on the unit disk with parameter . Restricting to the time…
Derivation of all structure constants for boundary Liouville CFT
Morris Ang, Guillaume Remy, Xin Sun +1
We prove that the probabilistic definition of the most general boundary three-point and bulk-boundary structure constants in Liouville conformal field theory (LCFT) agree respectiv…
The SLE loop via conformal welding of quantum disks
Morris Ang, Nina Holden, Xin Sun
We prove that the SLE loop measure arises naturally from the conformal welding of two -Liouville quantum gravity (LQG) disks for $γ^2 = κ\in (0,4)$. The proof relies on…
Liouville quantum gravity surfaces with boundary as matings of trees
Morris Ang, Ewain Gwynne
For , the quantum disk and -quantum wedge are two of the most natural types of Liouville quantum gravity (LQG) surfaces with boundary. These surfaces arise as scal…
Conformal welding of quantum disks and multiple SLE: the non-simple case
Morris Ang, Nina Holden, Xin Sun +1
Two-pointed quantum disks with a weight parameter is a canonical family of finite-volume random surfaces in Liouville quantum gravity. We extend the conformal welding of quan…
Comparison of discrete and continuum Liouville first passage percolation
Morris Ang
Discrete and continuum Liouville first passage percolation (DLFPP, LFPP) are two approximations of the conjectural -Liouville quantum gravity (LQG) metric, obtained by exponent…
SLE Loop Measure and Liouville Quantum Gravity
Morris Ang, Gefei Cai, Xin Sun +1
As recently shown by Holden and two of the authors, the conformal welding of two Liouville quantum gravity (LQG) disks produces a canonical variant of SLE curve whose law is called…
Brownian loops and the central charge of a Liouville random surface
Morris Ang, Minjae Park, Joshua Pfeffer +1
We explore the geometric meaning of the so-called zeta-regularized determinant of the Laplace-Beltrami operator on a compact surface, with or without boundary. We relate the $(-c/2…
The - relation in mating of trees
Morris Ang, Xin Sun, Pu Yu
In the mating-of-trees approach to Schramm-Loewner evolution (SLE) and Liouville quantum gravity (LQG), it is natural to consider two pairs of correlated Brownian motions coupled t…
Radial conformal welding in Liouville quantum gravity
Morris Ang, Pu Yu
The seminal work of Sheffield showed that when random surfaces called Liouville quantum gravity (LQG) are conformally welded, the resulting interface is Schramm-Loewner evolution (…
Integrability of SLE via conformal welding of random surfaces
Morris Ang, Nina Holden, Xin Sun
We demonstrate how to obtain integrable results for the Schramm-Loewner evolution (SLE) from Liouville conformal field theory (LCFT) and the mating-of-trees framework for Liouville…
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…
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…