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pro vyhledávání: '"Liouville quantum gravity"'
Autor:
Kavvadias, Konstantinos, Miller, Jason
We study the relationship between certain SLE$_\kappa(\rho)$ processes, which are variants of the Schramm-Loewner evolution with parameter $\kappa$ in which one keeps track of an extra marked point, and Liouville quantum gravity (LQG). These processe
Externí odkaz:
http://arxiv.org/abs/2412.04005
Autor:
Ang, Morris, Yu, Pu
The seminal work of Sheffield showed that when random surfaces called Liouville quantum gravity (LQG) are conformally welded, the resulting interface is Schramm-Loewner evolution (SLE). This has been proved for a variety of configurations, and has ap
Externí odkaz:
http://arxiv.org/abs/2411.19810
Autor:
Borga, Jacopo, Gwynne, Ewain
Permutons constructed from a Liouville quantum gravity surface and a pair of space-filling Schramm-Loewner evolutions (SLEs) have been shown -- or are conjectured -- to describe the scaling limit of various natural models of random constrained permut
Externí odkaz:
http://arxiv.org/abs/2409.15494
We study Liouville quantum gravity (LQG) in the supercritical (a.k.a. strongly coupled) phase, which has background charge $Q \in (0,2)$ and central charge $\mathbf{c}_{\mathrm{L}} = 1+6Q^2 \in (1,25)$. Recent works have shown how to define LQG in th
Externí odkaz:
http://arxiv.org/abs/2410.12693
As recently shown by Holden and two of the authors, the conformal welding of two Liouville quantum gravity (LQG) disks produces a canonical variant of SLE curve whose law is called the SLE loop measure. In this paper, we demonstrate how LQG can be us
Externí odkaz:
http://arxiv.org/abs/2409.16547
Autor:
Hip, Andres Contreras, Gwynne, Ewain
We investigate the notion of curvature in the context of Liouville quantum gravity (LQG) surfaces. We define the Gaussian curvature for LQG, which we conjecture is the scaling limit of discrete curvature on random planar maps. Motivated by this, we s
Externí odkaz:
http://arxiv.org/abs/2406.08674
We study fractal properties of support sets of the critical Liouville Quantum Gravity (cLQG) associated with the Gaussian Free Field in planar domains. Specifically, we completely characterize the gauge functions $\phi$ (subject to mild monotonicity
Externí odkaz:
http://arxiv.org/abs/2406.02814
Autor:
Berestycki, Nathanaël, Powell, Ellen
Over fourty years ago, the physicist Polyakov proposed a bold framework for string theory, in which the problem was reduced to the study of certain "random surfaces". He further made the tantalising suggestion that this theory could be explicitly sol
Externí odkaz:
http://arxiv.org/abs/2404.16642
Autor:
Hughes, Liam
Publikováno v:
Electron. Commun. Probab. 29 (2024), article no. 37, 1-13
We observe that non-doubling metric spaces can be characterized as those that contain arbitrarily large sets of approximately equidistant points and use this to show that, for $\gamma \in (0,2]$, the $\gamma$-Liouville quantum gravity metric is almos
Externí odkaz:
http://arxiv.org/abs/2312.12089
Autor:
Kammerer, Emmanuel
The purpose of this article is threefold. First, we show that when one explores a conformal loop ensemble of parameter $\kappa=4$ ($\mathrm{CLE}_4$) on an independent $2$-Liouville quantum gravity ($2$-LQG) disk, the surfaces which are cut out are in
Externí odkaz:
http://arxiv.org/abs/2311.08571