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The theory of the 2-dimensional Liouville Quantum Gravity, first introduced by Polyakov in his 1981 work has become a key notion in the study of random surfaces.
Quantum Geometry of bosonic strings
A. Polyakov · 1981
Earlier work this paper cites.
Sur le chaos multiplicatif
J.-P. Kahane · 1985
Earlier work this paper cites.
Notes on Quantum Liouville Theory and Quantum Gravity
N. Seiberg · 1990
Earlier work this paper cites.
Continuous Martingales and Brownian Motion
D. Revuz and M. Yor · 1991
Earlier work this paper cites.
Gaussian Hilbert spaces
S. Janson · 1997
Earlier work this paper cites.
A survey and some generalizations of Bessel processes
A. Göing-Jaeschke and M. Yor · 2003
Earlier work this paper cites.
Gaussian free field for mathematicians
S. Sheffield · 2007
Earlier work this paper cites.
Liouville Quantum Gravity and KPZ
B. Duplantier and S. Sheffield · 2011
Earlier work this paper cites.
Uniqueness and universality of the Brownian map
J.-F. Le Gall · 2013
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The Brownian map is the scaling limit of uniform random plane quadrangulations
G. Miermont · 2013
Earlier work this paper cites.
Equivalence of Liouville measure and Gaussian free field
N. Berestycki, S. Sheffield, and X. Sun · 2014
Cited alongside, same era.
Liouville quantum gravity as a mating of trees
B. Duplantier, J. Miller, and S. Sheffield · 2014
Cited alongside, same era.
Gaussian multiplicative chaos and applications: A review
R. Rhodes and V. Vargas · 2014
Cited alongside, same era.
Liouville Quantum Gravity on the Riemann Sphere
F. David, A. Kupiainen, R. Rhodes, and V. Vargas · 2016
Cited alongside, same era.
Liouville quantum gravity on complex tori
F. David, R. Rhodes, and V. Vargas · 2016
Cited alongside, same era.
Polyakov’s formulation of 2 d 2d bosonic string theory
Two Perspectives of the 2D Unit Area Quantum Sphere and Their Equivalence
J. Aru, Y. Huang, and X. Sun · 2017
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Compact Brownian surfaces I: Brownian disks
J. Bettinelli and G. Miermont · 2017
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Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees
J. Miller and S. Sheffield · 2017
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Liouville quantum gravity on the unit disk
Y. Huang, R. Rhodes, and V. Vargas · 2018
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Local Conformal Structure of Liouville Quantum Gravity
A. Kupiainen, R. Rhodes, and V. Vargas · 2019
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Liouville quantum gravity and the Brownian map I: The QLE(8/3,0) metric
J. Miller and S. Sheffield · 2019
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C. Guillarmou, R. Rhodes, and V. Vargas · 2016
Cited alongside, same era.
Liouville quantum gravity and the Brownian map II: geodesics and continuity of the embedding
J. Miller and S. Sheffield · 2016
Cited alongside, same era.
Liouville quantum gravity and the Brownian map III: the conformal structure is determined
J. Miller and S. Sheffield · 2016
Cited alongside, same era.
Lecture notes on Gaussian multiplicative chaos and Liouville Quantum Gravity
R. Rhodes and V. Vargas · 2016
Cited alongside, same era.
Conformal weldings of random surfaces: SLE and the quantum gravity zipper
S. Sheffield · 2016
Cited alongside, same era.
Tightness of Liouville first passage percolation for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
J. Ding, J. Dubédat, A. Dunlap, and H. Falconet · 2020
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Integrability of Liouville theory: proof of the DOZZ formula
A. Kupiainen, R. Rhodes, and V. Vargas · 2020
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Liouville quantum gravity surfaces with boundary as matings of trees
M. Ang and E. Gwynne · 2021
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Existence and uniqueness of the Liouville quantum gravity metric for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
E. Gwynne and J. Miller · 2021
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