96 citations · 215 across the 21 of their papers we have counts for
6 papers · 1 filter
SLE as a mating of trees in Euclidean geometry
Nina Holden, Xin Sun
The mating of trees approach to Schramm-Loewner evolution (SLE) in the random geometry of Liouville quantum gravity (LQG) has been recently developed by Duplantier-Miller-Sheffield…
How round are the complementary components of planar Brownian motion?
Nina Holden, Serban Nacu, Yuval Peres +1
Consider a Brownian motion in started from and run for time 1. Let denote the bounded connected components of . Let (re…
A distance exponent for Liouville quantum gravity
Ewain Gwynne, Nina Holden, Xin Sun
Let and let be the random distribution on which describes a -Liouville quantum gravity (LQG) cone. Also let and let be a whole-pl…
Dimension transformation formula for conformal maps into the complement of an SLE curve
Ewain Gwynne, Nina Holden, Jason Miller
We prove a formula relating the Hausdorff dimension of a deterministic Borel subset of and the Hausdorff dimension of its image under a conformal map from the upper hal…
Joint scaling limit of a bipolar-oriented triangulation and its dual in the peanosphere sense
Ewain Gwynne, Nina Holden, Xin Sun
Kenyon, Miller, Sheffield, and Wilson (2015) showed how to encode a random bipolar-oriented planar map by means of a random walk with a certain step size distribution. Using this e…
Sparse exchangeable graphs and their limits via graphon processes
Christian Borgs, Jennifer T. Chayes, Henry Cohn +1
In a recent paper, Caron and Fox suggest a probabilistic model for sparse graphs which are exchangeable when associating each vertex with a time parameter in . Here w…