Liouville quantum gravity as a mating of trees
There is a simple way to" glue together" a coupled pair of continuum random trees (CRTs) to
produce a topological sphere. The sphere comes equipped with a measure and a space …
produce a topological sphere. The sphere comes equipped with a measure and a space …
Liouville quantum gravity and the Brownian map I: the metric
J Miller, S Sheffield - Inventiones mathematicae, 2020 - Springer
Liouville quantum gravity (LQG) and the Brownian map (TBM) are two distinct models of
measure-endowed random surfaces. LQG is defined in terms of a real parameter γ γ, and it …
measure-endowed random surfaces. LQG is defined in terms of a real parameter γ γ, and it …
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 …
Conformal weldings of random surfaces: SLE and the quantum gravity zipper
S Sheffield - 2016 - projecteuclid.org
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 …
show that the interface between them is a random fractal curve called the Schramm …
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 …
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 …
Liouville quantum gravity and the Brownian map I: The QLE (8/3, 0) metric
J Miller, S Sheffield - arXiv preprint arXiv:1507.00719, 2015 - arxiv.org
Liouville quantum gravity (LQG) and the Brownian map (TBM) are two distinct models of
measure-endowed random surfaces. LQG is defined in terms of a real parameter $\gamma …
measure-endowed random surfaces. LQG is defined in terms of a real parameter $\gamma …
The Fyodorov–Bouchaud formula and Liouville conformal field theory
G Remy - 2020 - projecteuclid.org
In a remarkable paper in 2008, Fyodorov and Bouchaud conjectured an exact formula for
the density of the total mass of (subcritical) Gaussian multiplicative chaos (GMC) associated …
the density of the total mass of (subcritical) Gaussian multiplicative chaos (GMC) associated …
Liouville quantum gravity on the unit disk
Y Huang, R Rhodes, V Vargas - 2018 - projecteuclid.org
Our purpose is to pursue the rigorous construction of Liouville Quantum Field Theory on
Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context …
Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context …
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 …