46 citations · 292 across the 35 of their papers we have counts for
6 papers · 1 filter
Scaling limit of triangulations of polygons
Marie Albenque, Nina Holden, Xin Sun
We prove that random triangulations of types I, II, and III with a simple boundary under the critical Boltzmann weight converge in the scaling limit to the Brownian disk. The proof…
Mating of trees for random planar maps and Liouville quantum gravity: a survey
Ewain Gwynne, Nina Holden, Xin Sun
We survey the theory and applications of mating-of-trees bijections for random planar maps and their continuum analog: the mating-of-trees theorem of Duplantier, Miller, and Sheffi…
Liouville dynamical percolation
Christophe Garban, Nina Holden, Avelio Sepúlveda +1
We construct and analyze a continuum dynamical percolation process which evolves in a random environment given by a -Liouville measure. The homogeneous counterpart of this proce…
Convergence of uniform triangulations under the Cardy embedding
Nina Holden, Xin Sun
We consider an embedding of planar maps into an equilateral triangle which we call the Cardy embedding. The embedding is a discrete approximation of a conformal map based on pe…
Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense
Ewain Gwynne, Nina Holden, Xin Sun
Recent works have shown that random triangulations decorated by critical () Bernoulli site percolation converge in the scaling limit to a -Liouville quantum grav…
Weak LQG metrics and Liouville first passage percolation
Julien Dubédat, Hugo Falconet, Ewain Gwynne +2
For , we define a weak -Liouville quantum gravity (LQG) metric to be a function which takes in an instance of the planar Gaussian free field (GFF) and…