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Sparse Exchangeable Graphs and Their Limits via Graphon Processes

- C. Borgs, J. Chayes, Henry Cohn, N. Holden
- MathematicsJ. Mach. Learn. Res.
- 26 January 2016

TLDR

Subpolynomial trace reconstruction for random strings and arbitrary deletion probability

- N. Holden, R. Pemantle, Y. Peres
- Computer Science, MathematicsCOLT
- 15 January 2018

TLDR

Lower bounds for trace reconstruction

TLDR

Convergence of uniform triangulations under the Cardy embedding

We consider an embedding of planar maps into an equilateral triangle $\Delta$ which we call the Cardy embedding. The embedding is a discrete approximation of a conformal map based on percolation… Expand

Joint scaling limit of a bipolar-oriented triangulation and its dual in the peanosphere sense

- Ewain Gwynne, N. Holden, Xin Sun
- Mathematics
- 3 March 2016

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 encoding together… Expand

A distance exponent for Liouville quantum gravity

- Ewain Gwynne, N. Holden, Xin Sun
- Mathematics
- 3 June 2016

Let $$\gamma \in (0,2)$$γ∈(0,2) and let h be the random distribution on $$\mathbb C$$C which describes a $$\gamma $$γ-Liouville quantum gravity (LQG) cone. Also let $$\kappa = 16/\gamma ^2… Expand

An almost sure KPZ relation for SLE and Brownian motion

- Ewain Gwynne, N. Holden, Jason Miller
- MathematicsThe Annals of Probability
- 3 December 2015

The peanosphere construction of Duplantier, Miller, and Sheffield provides a means of representing a $\gamma$-Liouville quantum gravity (LQG) surface, $\gamma \in (0,2)$, decorated with a… Expand

Mating of trees for random planar maps and Liouville quantum gravity: a survey

- Ewain Gwynne, N. Holden, Xin Sun
- Mathematics
- 10 October 2019

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 Sheffield (2014). The… Expand

A mating-of-trees approach for graph distances in random planar maps

- Ewain Gwynne, N. Holden, Xin Sun
- MathematicsProbability Theory and Related Fields
- 2 November 2017

We introduce a general technique for proving estimates for certain random planar maps which belong to the $$\gamma $$ γ -Liouville quantum gravity (LQG) universality class for $$\gamma \in (0,2)$$ γ… Expand

Liouville Quantum Gravity with Matter Central Charge in (1, 25): A Probabilistic Approach

- Ewain Gwynne, N. Holden, Joshua Pfeffer, G. Remy
- MathematicsCommunications in Mathematical Physics
- 21 March 2019

There is a substantial literature concerning Liouville quantum gravity (LQG) in two dimensions with conformal matter field of central charge $${{\mathbf {c}}}_{\mathrm M} \in (-\infty ,1]$$ c M ∈ ( -… Expand

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