Existence and uniqueness of the Liouville quantum gravity metric for
We show that for each γ ∈ (0, 2) γ∈(0, 2), there is a unique metric (ie, distance function)
associated with γ γ-Liouville quantum gravity (LQG). More precisely, we show that for the …
associated with γ γ-Liouville quantum gravity (LQG). More precisely, we show that for the …
Integrability of Liouville theory: proof of the DOZZ formula
A Kupiainen, R Rhodes, V Vargas - Annals of Mathematics, 2020 - projecteuclid.org
Dorn and Otto (1994) and independently Zamolodchikov and Zamolodchikov (1996)
proposed a remarkable explicit expression, the so-called-M DOZZ formula, for the three …
proposed a remarkable explicit expression, the so-called-M DOZZ formula, for the three …
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 …
Conformal bootstrap in Liouville theory
C Guillarmou, A Kupiainen, R Rhodes… - arXiv preprint arXiv …, 2020 - arxiv.org
The conformal bootstrap hypothesis is a powerful idea in theoretical physics which has led
to spectacular predictions in the context of critical phenomena. It postulates an explicit …
to spectacular predictions in the context of critical phenomena. It postulates an explicit …
Segal's axioms and bootstrap for Liouville Theory
C Guillarmou, A Kupiainen, R Rhodes… - arXiv preprint arXiv …, 2021 - arxiv.org
In 1987 Graeme Segal gave a functorial definition of Conformal Field Theory (CFT) that was
designed to capture the mathematical essence of the Conformal Bootstrap formalism …
designed to capture the mathematical essence of the Conformal Bootstrap formalism …
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 …
establishing exact formulas for two CLE observables. The first describes the joint moments …
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 …
FZZ formula of boundary Liouville CFT via conformal welding
Liouville Conformal Field Theory (LCFT) on the disk describes the conformal factor of the
quantum disk, which is the natural random surface in Liouville quantum gravity with disk …
quantum disk, which is the natural random surface in Liouville quantum gravity with disk …
Maxima of log-correlated fields: some recent developments
EC Bailey, JP Keating - Journal of Physics A: Mathematical and …, 2022 - iopscience.iop.org
We review recent progress relating to the extreme value statistics of the characteristic
polynomials of random matrices associated with the classical compact groups, and of the …
polynomials of random matrices associated with the classical compact groups, and of the …