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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.
Convergence of uniform triangulations under the Cardy embedding
N. Holden and X. Sun · 1905
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Mating of trees for random planar maps and Liouville quantum gravity: a survey
E. Gwynne, N. Holden, and X. Sun · 1910
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Quantum geometry of bosonic strings
A. M. Polyakov · 1981
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A decomposition of Bessel bridges
J. Pitman and M. Yor · 1982
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Sur le chaos multiplicatif
J.-P. Kahane · 1985
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Conformal field theories coupled to 2-D gravity in the conformal gauge
F. David · 1988
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Conformal field theory and 2D quantum gravity
J. Distler and H. Kawai · 1989
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Size-biased sampling of Poisson point processes and excursions
M. Perman, J. Pitman, and M. Yor · 1992
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Lévy processes
J. Bertoin · 1996
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Scaling limits of loop-erased random walks and uniform spanning trees
O. Schramm · 2000
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Foundations of modern probability
O. Kallenberg · 2002
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Conformal restriction: the chordal case
G. Lawler, O. Schramm, and W. Werner · 2003
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The Brownian loop soup
G. F. Lawler and W. Werner · 2004
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SLE ( κ , ρ ) {\rm SLE}(\kappa,\rho) martingales and duality
J. Dubédat · 2005
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D. Zhan · 2008
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Gaussian multiplicative chaos revisited
R. Robert and V. Vargas · 2010
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Liouville quantum gravity and KPZ
B. Duplantier and S. Sheffield · 2011
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Gaussian multiplicative chaos and applications: A review
R. Rhodes and V. Vargas · 2014
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An almost sure KPZ relation for SLE and Brownian motion
E. Gwynne, N. Holden, and J. Miller · 2015
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Convergence of the self-avoiding walk on random quadrangulations to SLE 8/3
E. Gwynne and J. Miller · 2016
Harmonic functions on mated-CRT maps
E. Gwynne, J. Miller, and S. Sheffield · 2019
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Uniqueness of the welding problem for SLE and Liouville quantum gravity
O. McEnteggart, J. Miller, and W. Qian · 2019
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Liouville quantum gravity spheres as matings of finite-diameter trees
J. Miller and S. Sheffield · 2019
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Random walks on mated-CRT planar maps and Liouville Brownian motion
N. Berestycki and E. Gwynne · 2020
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Ising model on random triangulations of the disk: phase transition
L. Chen and J. Turunen · 2020
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Imaginary geometry I: interacting SLEs
J. Miller and S. Sheffield · 2016
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J. Miller and S. Sheffield · 2016
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Conformal weldings of random surfaces: SLE and the quantum gravity zipper
S. Sheffield · 2016
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Quantum gravity and inventory accumulation
S. Sheffield · 2016
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Schramm-Loewner evolution
A. Kemppainen · 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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Natural parametrization of SLE: the Gaussian free field point of view
S. Benoist · 2018
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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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Liouville quantum gravity as a mating of trees
B. Duplantier, J. Miller, and S. Sheffield · 2020
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Simple Conformal Loop Ensembles on Liouville Quantum Gravity
J. Miller, S. Sheffield, and W. Werner · 2020
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Integrability of boundary Liouville conformal field theory
G. Remy and T. Zhu · 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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Integrability of SLE via conformal welding of random surfaces
M. Ang, N. Holden, and X. Sun · 2021
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FZZ formula of boundary Liouville CFT via conformal welding
M. Ang, G. Remy, and X. Sun · 2021
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Integrability of the conformal loop ensemble
M. Ang and X. Sun · 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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SLE loop measures
D. Zhan · 2021
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