• Corpus ID: 221761489

Conformal welding of quantum disks

@article{Ang2020ConformalWO,
  title={Conformal welding of quantum disks},
  author={Morris Ang and Nina Holden and Xin Sun},
  journal={arXiv: Probability},
  year={2020}
}
Two-pointed quantum disks are a family of finite-area random surfaces that arise naturally in Liouville quantum gravity. In this paper we show that conformally welding two quantum disks according to their boundary lengths gives another quantum disk decorated with a chordal SLE curve. This extends the classical result of Sheffield (2010) and Duplantier-Miller-Sheffield (2014) on the welding of infinite-area two-pointed quantum surfaces, which is fundamental to the mating-of-trees theory. Our… 
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References

SHOWING 1-10 OF 57 REFERENCES
Conformal weldings of random surfaces: SLE and the quantum gravity zipper
We construct a conformal welding of two Liouville quantum gravity random surfaces and show that the interface between them is a random fractal curve called the Schramm-Loewner evolution (SLE),
Liouville quantum gravity surfaces with boundary as matings of trees
  • M. Ang, Ewain Gwynne
  • Physics, Mathematics
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
  • 2021
For $\gamma \in (0,2)$, the quantum disk and $\gamma$-quantum wedge are two of the most natural types of Liouville quantum gravity (LQG) surfaces with boundary. These surfaces arise as scaling limits
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 (2014). The
Simple conformal loop ensembles on Liouville quantum gravity
We show that when one draws a simple conformal loop ensemble (CLE$_\kappa$ for $\kappa \in (8/3,4)$) on an independent $\sqrt{\kappa}$-Liouville quantum gravity (LQG) surface and explores the CLE in
Liouville quantum gravity and KPZ
AbstractConsider a bounded planar domain D, an instance h of the Gaussian free field on D, with Dirichlet energy (2π)−1∫D∇h(z)⋅∇h(z)dz, and a constant 0≤γ<2. The Liouville quantum gravity measure on
Conformal restriction: The chordal case
We characterize and describe all random subsets K of a given simply connected planar domain (the upper half-plane Η, say) which satisfy the conformal restriction” property, i.e., K connects two fixed
Integrability of the conformal loop ensemble
We demonstrate that the conformal loop ensemble (CLE) has a rich integrable structure by establishing exact formulas for two CLE observables. The first describes the joint moments of the conformal
Convergence of the free Boltzmann quadrangulation with simple boundary to the Brownian disk
We prove that the free Boltzmann quadrangulation with simple boundary and fixed perimeter, equipped with its graph metric, natural area measure, and the path which traces its boundary converges in
Ising model on random triangulations of the disk: phase transition
In [arXiv:1806.06668], we have studied the Boltzmann random triangulation of the disk coupled to an Ising model with Dobrushin boundary condition at its critical temperature. In this paper, we
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