Mating of trees for random planar maps and Liouville quantum gravity: a survey
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 …
and their continuum analog: the mating-of-trees theorem of Duplantier, Miller, and Sheffield …
Introduction to the Liouville quantum gravity metric
Liouville quantum gravity (LQG) is a one-parameter family of models of random fractal
surfaces which first appeared in the physics literature in the 1980s. Recent works have …
surfaces which first appeared in the physics literature in the 1980s. Recent works have …
Uniqueness of the critical and supercritical Liouville quantum gravity metrics
We show that for each c M∈ 1, 25) c_M∈1,25), there is a unique metric associated with
Liouville quantum gravity (LQG) with matter central charge c M c_M. An earlier series of …
Liouville quantum gravity (LQG) with matter central charge c M c_M. An earlier series of …
Schnyder woods, SLE (16), and Liouville quantum gravity
Y Li, X Sun, SS Watson - arXiv preprint arXiv:1705.03573, 2017 - arxiv.org
In 1990, Schnyder used a 3-spanning-tree decomposition of a simple triangulation, now
known as the Schnyder wood, to give a fundamental grid-embedding algorithm for planar …
known as the Schnyder wood, to give a fundamental grid-embedding algorithm for planar …
Moments of the 2D directed polymer in the subcritical regime and a generalisation of the Erdös–Taylor theorem
D Lygkonis, N Zygouras - Communications in Mathematical Physics, 2023 - Springer
We compute the limit of the moments of the partition function ZN β N of the directed polymer
in dimension d= 2 in the subcritical regime, ie when the inverse temperature is scaled as β …
in dimension d= 2 in the subcritical regime, ie when the inverse temperature is scaled as β …
The 27 geodesic networks in the directed landscape
D Dauvergne - arXiv preprint arXiv:2302.07802, 2023 - arxiv.org
The directed landscape is a random directed metric on the plane that arises as the scaling
limit of classical metric models in the KPZ universality class. Typical pairs of points in the …
limit of classical metric models in the KPZ universality class. Typical pairs of points in the …
Uniqueness of the critical long-range percolation metrics
J Ding, Z Fan, LJ Huang - arXiv preprint arXiv:2308.00621, 2023 - arxiv.org
In this work, we study the random metric for the critical long-range percolation on $\mathbb
{Z}^ d $. A recent work by B\" aumler [3] implies the subsequential scaling limit, and our main …
{Z}^ d $. A recent work by B\" aumler [3] implies the subsequential scaling limit, and our main …
Conformally invariant fields out of Brownian loop soups
A Jego, T Lupu, W Qian - arXiv preprint arXiv:2307.10740, 2023 - arxiv.org
Consider a Brownian loop soup $\mathcal {L} _D^\theta $ with subcritical intensity $\theta\in
(0, 1/2] $ in some 2D bounded simply connected domain. We define and study the …
(0, 1/2] $ in some 2D bounded simply connected domain. We define and study the …
The Yang-Mills heat flow with random distributional initial data
S Cao, S Chatterjee - Communications in Partial Differential …, 2023 - Taylor & Francis
We construct local solutions to the Yang–Mills heat flow (in the DeTurck gauge) for a certain
class of random distributional initial data, which includes the 3D Gaussian free field. The …
class of random distributional initial data, which includes the 3D Gaussian free field. The …
What is a random surface?
S Sheffield - Plenary LectureS, 2022 - ems.press
Given 2n unit equilateral triangles, there are finitely many ways to glue each edge to a
partner. We obtain a random sphere-homeomorphic surface by sampling uniformly from the …
partner. We obtain a random sphere-homeomorphic surface by sampling uniformly from the …