96 citations · 215 across the 21 of their papers we have counts for
7 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…
Liouville quantum gravity with matter central charge in : a probabilistic approach
Ewain Gwynne, Nina Holden, Joshua Pfeffer +1
There is a substantial literature concerning Liouville quantum gravity (LQG) in two dimensions with conformal matter field of central charge ${\mathbf{c}}_{\mathrm M}\in(-\infty,1]…
Communication cost of consensus for nodes with limited memory
Giulia Fanti, Nina Holden, Yuval Peres +1
Motivated by applications in blockchains and sensor networks, we consider a model of nodes trying to reach consensus on their majority bit. Each node is assigned a bit at t…