96 citations · 215 across the 21 of their papers we have counts for
40 papers
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…
Matrix Product State Representatives of Symmetry-Protected Phases
Thomas Jackson
We provide a simple ansatz for finding integer spin -invariant matrix product states representing a phase for each triple of topological indic…
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…
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…
The SLE loop via conformal welding of quantum disks
Morris Ang, Nina Holden, Xin Sun
We prove that the SLE loop measure arises naturally from the conformal welding of two -Liouville quantum gravity (LQG) disks for . The proof relies on our…
Liouville quantum gravity weighted by conformal loop ensemble nesting statistics
Nina Holden, Matthis Lehmkuehler
We study Liouville quantum gravity (LQG) surfaces whose law has been reweighted according to nesting statistics for a conformal loop ensemble (CLE) relative to …
Baxter permuton and Liouville quantum gravity
Jacopo Borga, Nina Holden, Xin Sun +1
The Baxter permuton is a random probability measure on the unit square which describes the scaling limit of uniform Baxter permutations. We find an explict formula for the expectat…
Mating of trees for critical Liouville quantum gravity
Juhan Aru, Nina Holden, Ellen Powell +1
In a groundbreaking work, Duplantier, Miller and Sheffield showed that subcritical Liouville quantum gravity (LQG) coupled with Schramm-Loewner evolutions (SLE) can be described by…
Integrability of SLE via conformal welding of random surfaces
Morris Ang, Nina Holden, Xin Sun
We demonstrate how to obtain integrable results for the Schramm-Loewner evolution (SLE) from Liouville conformal field theory (LCFT) and the mating-of-trees framework for Liouville…
Conformal welding of quantum disks
Morris Ang, Nina Holden, Xin Sun
Two-pointed quantum disks with a weight parameter are a family of finite-area random surfaces that arise naturally in Liouville quantum gravity. In this paper we show that…
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…
Conformal welding for critical Liouville quantum gravity
Nina Holden, Ellen Powell
Consider two critical Liouville quantum gravity surfaces (i.e., -LQG for ), each with the topology of and with infinite boundary length. We prove that there a.…
Recurrent extensions of real-valued self-similar Markov processes
Henry Pantí, Juan Carlos Pardo, Víctor Manuel Rivero
Let be a self-similar Markov process taking values in such that the state 0 is a trap. In this paper, we present a necessary and sufficient conditio…
Percolation on triangulations: a bijective path to Liouville quantum gravity
Olivier Bernardi, Nina Holden, Xin Sun
We set the foundation for a series of works aimed at proving strong relations between uniform random planar maps and Liouville quantum gravity (LQG). Our method relies on a bijecti…