4 papers
Joint scaling limit of a bipolar-oriented triangulation and its dual in the peanosphere sense
Ewain Gwynne, Nina Holden, Xin Sun
Kenyon, Miller, Sheffield, and Wilson (2015) showed how to encode a random bipolar-oriented planar map by means of a random walk with a certain step size distribution. Using this e…
Permutons, meanders, and SLE-decorated Liouville quantum gravity
Jacopo Borga, Ewain Gwynne, Xin Sun
We study a class of random permutons which can be constructed from a pair of space-filling Schramm-Loewner evolution (SLE) curves on a Liouville quantum gravity (LQG) surface. This…
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…
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…