Critical Gaussian multiplicative chaos: a review
E Powell - arXiv preprint arXiv:2006.13767, 2020 - arxiv.org
arXiv:2006.13767v3 [math.PR] 2 Jul 2020 Page 1 arXiv:2006.13767v3 [math.PR] 2 Jul 2020
Critical Gaussian multiplicative chaos: a review Ellen Powell∗ Abstract This review-style article …
Critical Gaussian multiplicative chaos: a review Ellen Powell∗ Abstract This review-style article …
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 …
Integrability of SLE via conformal welding of random surfaces
We demonstrate how to obtain integrability results for the Schramm‐Loewner evolution
(SLE) from Liouville conformal field theory (LCFT) and the mating‐of‐trees framework for …
(SLE) from Liouville conformal field theory (LCFT) and the mating‐of‐trees framework for …
Conformal welding of quantum disks
Two-pointed quantum disks with a weight parameter W> 0 are a family of finite-area random
surfaces that arise naturally in Liouville quantum gravity. In this paper we show that …
surfaces that arise naturally in Liouville quantum gravity. In this paper we show that …
Supercritical Liouville quantum gravity and CLE
We establish the first relationship between Schramm-Loewner evolution (SLE) and Liouville
quantum gravity (LQG) in the supercritical (aka strongly coupled) phase, which corresponds …
quantum gravity (LQG) in the supercritical (aka strongly coupled) phase, which corresponds …
The critical Liouville quantum gravity metric induces the Euclidean topology
We show that every possible metric associated with critical (γ= 2) Liouville quantum gravity
(LQG) induces the same topology on the plane as the Euclidean metric. More precisely, we …
(LQG) induces the same topology on the plane as the Euclidean metric. More precisely, we …
Conformal removability of non-simple Schramm-Loewner evolutions
We consider the Schramm-Loewner evolution (SLE $ _\kappa $) for $\kappa\in (4, 8) $,
which is the regime that the curve is self-intersecting but not space-filling. We let ${\mathcal …
which is the regime that the curve is self-intersecting but not space-filling. We let ${\mathcal …
Liouville conformal field theory and the quantum zipper
M Ang - arXiv preprint arXiv:2301.13200, 2023 - arxiv.org
Sheffield showed that conformally welding a $\gamma $-Liouville quantum gravity (LQG)
surface to itself gives a Schramm-Loewner evolution (SLE) curve with parameter …
surface to itself gives a Schramm-Loewner evolution (SLE) curve with parameter …
Uniqueness of the welding problem for SLE and Liouville quantum gravity
UNIQUENESS OF THE WELDING PROBLEM FOR SLE AND LIOUVILLE QUANTUM
GRAVITY Page 1 J. Inst. Math. Jussieu (2021) 20(3), 757–783 doi:10.1017/S1474748019000331 …
GRAVITY Page 1 J. Inst. Math. Jussieu (2021) 20(3), 757–783 doi:10.1017/S1474748019000331 …
Conformal removability of SLE
We consider the Schramm-Loewner evolution (SLE $ _\kappa $) with $\kappa= 4$, the
critical value of $\kappa> 0$ at or below which SLE $ _\kappa $ is a simple curve and above …
critical value of $\kappa> 0$ at or below which SLE $ _\kappa $ is a simple curve and above …