N. Holden

activity

20152026

most citedSparse exchangeable graphs and their limits via graphon processes

96 citations · 215 across the 21 of their papers we have counts for

collaborators

Showing 2018Show all

8 papers · 1 filter

math.PR2018★ 16 cited

Conformal welding for critical Liouville quantum gravity

Nina Holden, Ellen Powell

Consider two critical Liouville quantum gravity surfaces (i.e., $γ$ -LQG for $γ = 2$ ), each with the topology of $H$ and with infinite boundary length. We prove that there a.…

math.PR2018

Recurrent extensions of real-valued self-similar Markov processes

Henry Pantí, Juan Carlos Pardo, Víctor Manuel Rivero

Let $X = (X_{t}, t \geq 0)$ be a self-similar Markov process taking values in $R$ such that the state 0 is a trap. In this paper, we present a necessary and sufficient conditio…

math.PR2018

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…

math.PR2018★ 2 cited

Negative moments for Gaussian multiplicative chaos on fractal sets

Christophe Garban, Nina Holden, Avelio Sepúlveda +1

The objective of this note is to study the probability that the total mass of a sub-critical Gaussian multiplicative chaos (GMC) with arbitrary base measure $σ$ is small. When $σ$ …

math.PR2018★ 1 cited

Natural parametrization of percolation interface and pivotal points

Nina Holden, Xinyi Li, Xin Sun

We prove that the interface of critical site percolation on the triangular lattice converges to SLE $_{6}$ in its natural parametrization, where the discrete interface is parametrized…

math.PR2018★ 6 cited

Minkowski content of Brownian cut points

Nina Holden, Gregory F. Lawler, Xinyi Li +1

Let $W (t)$ , $0 \leq t \leq T$ , be a Brownian motion in $R^{d}$ , $d = 2, 3$ . We say that $x$ is a cut point for $W$ if $x = W (t)$ for some $t \in (0, T)$ such that $W [0, t)$ and $W (t…

math.PR2018

Scaling limits of the Schelling model

Nina Holden, Scott Sheffield

The Schelling model, introduced by Schelling in 1969 as a model for residential segregation in cities, describes how populations of multiple types self-organize to form homogeneous…

math.PR2018

Subpolynomial trace reconstruction for random strings and arbitrary deletion probability

Nina Holden, Robin Pemantle, Yuval Peres +1

The insertion-deletion channel takes as input a bit string $x \in {0, 1}^{n}$ , and outputs a string where bits have been deleted and inserted independently at random. The trac…