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Recent work has shown that for $\gamma \in (0,2)$, a Liouville quantum gravity (LQG) surface can be endowed with a canonical metric.
Bounds for distances and geodesic dimension in Liouville first passage percolation
E. Gwynne and J. Pfeffer · 1903
Earlier work this paper cites.
Tightness of Liouville first passage percolation for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
J. Ding, J. Dubédat, A. Dunlap, and H. Falconet · 1904
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Weak LQG metrics and Liouville first passage percolation
J. Dubédat, H. Falconet, E. Gwynne, J. Pfeffer, and X. Sun · 1905
Earlier work this paper cites.
Confluence of geodesics in Liouville quantum gravity for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
E. Gwynne and J. Miller · 1905
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Local metrics of the Gaussian free field
E. Gwynne and J. Miller · 1905
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Conformal covariance of the Liouville quantum gravity metric for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
E. Gwynne and J. Miller · 1905
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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 · 1905
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Random surfaces and Liouville quantum gravity
E. Gwynne · 1908
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The Dimension of the Boundary of a Liouville Quantum Gravity Metric Ball
E. Gwynne · 1909
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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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Sur le chaos multiplicatif
J.-P. Kahane · 1985
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Boundary behaviour of conformal maps
C. Pommerenke · 1992
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Volume of metric balls in Liouville quantum gravity
M. Ang, H. Falconet, and X. Sun · 2001
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A course in metric geometry
D. Burago, Y. Burago, and S. Ivanov · 2001
Cited alongside, same era.
On the independence number of a graph in terms of order and size
J. Harant and I. Schiermeyer · 2001
Cited alongside, same era.
Tightness of supercritical Liouville first passage percolation
J. Ding and E. Gwynne · 2005
Cited alongside, same era.
Geodesics in the Brownian map: Strong confluence and geometric structure
J. Miller and W. Qian · 2008
Cited alongside, same era.
Geodesics and metric ball boundaries in Liouville quantum gravity
E. Gwynne, J. Pfeffer, and S. Sheffield · 2010
Cited alongside, same era.
Liouville quantum gravity and the Brownian map III: the conformal structure is determined
J. Miller and S. Sheffield · 2016
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Stability of geodesics in the Brownian map
O. Angel, B. Kolesnik, and G. Miermont · 2017
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Compact Brownian surfaces I: Brownian disks
J. Bettinelli and G. Miermont · 2017
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E. Gwynne and J. Miller · 2017
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Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees
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J.-F. Le Gall · 2010
Cited alongside, same era.
Liouville quantum gravity and KPZ
B. Duplantier and S. Sheffield · 2011
Cited alongside, same era.
Uniqueness and universality of the Brownian map
J.-F. Le Gall · 2013
Cited alongside, same era.
The Brownian map is the scaling limit of uniform random plane quadrangulations
G. Miermont · 2013
Cited alongside, same era.
Gaussian multiplicative chaos and applications: A review
R. Rhodes and V. Vargas · 2014
Cited alongside, same era.
An axiomatic characterization of the Brownian map
J. Miller and S. Sheffield · 2015
Cited alongside, same era.
Boundary of bounded connected open subset of ℝ n \mathbb{R}^{n} , whose complement is also connected, is connected
M. Kohan · 2016
Cited alongside, same era.
J. Miller and S. Sheffield · 2017
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Lecture notes on Liouville theory and the DOZZ formula
V. Vargas · 2017
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The fractal dimension of Liouville quantum gravity: universality, monotonicity, and bounds
J. Ding and E. Gwynne · 2018
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Classification of scaling limits of uniform quadrangulations with a boundary
E. Baur, G. Miermont, and G. Ray · 2019
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Heat kernel for Liouville Brownian motion and Liouville graph distance
J. Ding, O. Zeitouni, and F. Zhang · 2019
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KPZ formulas for the Liouville quantum gravity metric
E. Gwynne and J. Pfeffer · 2019
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The geodesics in Liouville quantum gravity are not Schramm-Loewner evolutions
J. Miller and W. Qian · 2020
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Liouville quantum gravity and the Brownian map I: the QLE ( 8 / 3 , 0 ) {\rm QLE}(8/3,0) metric
J. Miller and S. Sheffield · 2020
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Regularity and confluence of geodesics for the supercritical Liouville quantum gravity metric
J. Ding and E. Gwynne · 2021
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