5 papers
Circle packing and Riemann uniformization of random planar maps in an ergodic scale-free environment
Nina Holden, Pu Yu
We prove that embedded infinite planar maps in ergodic scale-free environments are close to their circle packing and Riemann uniformization embedding on a large scale, as long as s…
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…
Liouville quantum gravity: from random planar maps to conformal field theory
Nina Holden, Xin Sun
Originating in theoretical physics, Liouville quantum gravity (LQG) has been an important topic in probability theory and mathematical physics in the past two decades. In this proc…
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…
Regularity of the Schramm-Loewner evolution: Up-to-constant variation and modulus of continuity
Nina Holden, Yizheng Yuan
We find optimal (up to constant) bounds for the following measures for the regularity of the Schramm-Loewner evolution (SLE): variation regularity, modulus of continuity, and law o…