96 citations · 215 across the 21 of their papers we have counts for
4 papers · 2 filters
The circle packing and Riemann uniformization embedding of the tree-weighted planar maps converges to Liouville quantum gravity
Nina Holden, Pu Yu
We prove that in the disk, sphere, whole-plane topology, spanning tree weighted planar maps converge to -Liouville quantum gravity disk, sphere or cone under circle packi…
The Tutte embedding of tree-weighted planar maps converges to Liouville quantum gravity
Nina Holden
Suppose is a planar map with a macroscopic boundary decorated by a spanning tree , such that has been sampled from the critical Boltzman measure. We show that co…
Oriented planar maps and annular mating of trees
Xingjian Di, Nina Holden, Zhenfeng Tu +1
We study a class of oriented annular planar maps which are closely related to bipolar-oriented maps. We prove that such maps can be encoded by a 2D lattice walk which converges to…
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…