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We show that for each $\gamma \in (0,2)$, there is a unique metric (i.e., distance function) associated with $\gamma$-Liouville quantum gravity (LQG).
Liouville quantum gravity with matter central charge in ( 1 , 25 ) (1,25) : a probabilistic approach
E. Gwynne, N. Holden, J. Pfeffer, and G. Remy · 1903
Earlier work this paper cites.
Bounds for distances and geodesic dimension in Liouville first passage percolation
E. Gwynne and J. Pfeffer · 1903
Earlier work this paper cites.
Comparison of discrete and continuum Liouville first passage percolation
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Earlier work this paper cites.
Tightness of Liouville first passage percolation for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
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Earlier work this paper cites.
Weak LQG metrics and Liouville first passage percolation
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Earlier work this paper cites.
Confluence of geodesics in Liouville quantum gravity for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
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Earlier work this paper cites.
Conformal covariance of the Liouville quantum gravity metric for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
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Earlier work this paper cites.
Local metrics of the Gaussian free field
E. Gwynne and J. Miller · 1905
Earlier work this paper cites.
The dimension of the boundary of a Liouville quantum gravity metric ball
E. Gwynne · 1909
Earlier work this paper cites.
Unit boundary length quantum disk: a study of two different perspectives and their equivalence
B. Cerclé · 1912
Earlier work this paper cites.
Planar maps are well labeled trees
R. Cori and B. Vauquelin · 1981
Earlier work this paper cites.
Quantum geometry of bosonic strings
A. M. Polyakov · 1981
Earlier work this paper cites.
Quantum geometry of fermionic strings
A. M. Polyakov · 1981
Earlier work this paper cites.
Sur le chaos multiplicatif
J.-P. Kahane · 1985
Earlier work this paper cites.
Fractal structure of 2D-quantum gravity
V. Knizhnik, A. Polyakov, and A. Zamolodchikov · 1988
Earlier work this paper cites.
Analytic study of fractal structure of quantized surface in two-dimensional quantum gravity
Y. Watabiki · 1992
Earlier work this paper cites.
Bijective census and random generation of Eulerian planar maps with prescribed vertex degrees
G. Schaeffer · 1997
Earlier work this paper cites.
Volume of metric balls in Liouville quantum gravity
M. Ang, H. Falconet, and X. Sun · 2001
Earlier work this paper cites.
A course in metric geometry
D. Burago, Y. Burago, and S. Ivanov · 2001
Earlier work this paper cites.
Planar maps as labeled mobiles
J. Bouttier, P. Di Francesco, and E. Guitter · 2004
Earlier work this paper cites.
Tightness of supercritical Liouville first passage percolation
J. Ding and E. Gwynne · 2005
Earlier work this paper cites.
Limit of normalized quadrangulations: the Brownian map
J.-F. Marckert and A. Mokkadem · 2006
Earlier work this paper cites.
The topological structure of scaling limits of large planar maps
J.-F. Le Gall · 2007
Earlier work this paper cites.
Gaussian free fields for mathematicians
S. Sheffield · 2007
Earlier work this paper cites.
SLE and the free field: partition functions and couplings
J. Dubédat · 2009
Earlier work this paper cites.
Thick points of the Gaussian free field
X. Hu, J. Miller, and Y. Peres · 2010
Earlier work this paper cites.
Geodesics in large planar maps and in the Brownian map
J.-F. Le Gall · 2010
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
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A contour line of the continuum Gaussian free field
O. Schramm and S. Sheffield · 2013
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Equivalence of Liouville measure and Gaussian free field
N. Berestycki, S. Sheffield, and X. Sun · 2014
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Liouville quantum gravity as a mating of trees
B. Duplantier, J. Miller, and S. Sheffield · 2014
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Stability of geodesics in the Brownian map
O. Angel, B. Kolesnik, and G. Miermont · 2017
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An elementary approach to Gaussian multiplicative chaos
N. Berestycki · 2017
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Compact Brownian surfaces I: Brownian disks
J. Bettinelli and G. Miermont · 2017
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A mating-of-trees approach for graph distances in random planar maps
E. Gwynne, N. Holden, and X. Sun · 2017
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Random walk on random planar maps: spectral dimension, resistance, and displacement
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Log-correlated Gaussian fields: an overview
B. Duplantier, R. Rhodes, S. Sheffield, and V. Vargas · 2014
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Critical Gaussian multiplicative chaos: convergence of the derivative martingale
B. Duplantier, R. Rhodes, S. Sheffield, and V. Vargas · 2014
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Renormalization of critical Gaussian multiplicative chaos and KPZ relation
B. Duplantier, R. Rhodes, S. Sheffield, and V. Vargas · 2014
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On the heat kernel and the Dirichlet form of Liouville Brownian motion
C. Garban, R. Rhodes, and V. Vargas · 2014
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Gaussian multiplicative chaos and applications: A review
R. Rhodes and V. Vargas · 2014
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Diffusion in planar Liouville quantum gravity
N. Berestycki · 2015
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An axiomatic characterization of the Brownian map
J. Miller and S. Sheffield · 2015
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E. Gwynne and J. Miller · 2017
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The Tutte embedding of the mated-CRT map converges to Liouville quantum gravity
E. Gwynne, J. Miller, and S. Sheffield · 2017
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Integrability of Liouville theory: proof of the DOZZ Formula
A. Kupiainen, R. Rhodes, and V. Vargas · 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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The Fyodorov-Bouchaud formula and Liouville conformal field theory
G. Remy · 2017
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Subsequential scaling limits for Liouville graph distance
J. Ding and A. Dunlap · 2018
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Liouville metric of star-scale invariant fields: tails and Weyl scaling
J. Dubédat and H. Falconet · 2018
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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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Heat kernel for Liouville Brownian motion and Liouville graph distance
J. Ding, O. Zeitouni, and F. Zhang · 2018
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Anomalous diffusion of random walk on random planar maps
E. Gwynne and T. Hutchcroft · 2018
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Liouville quantum gravity on the unit disk
Y. Huang, R. Rhodes, and V. Vargas · 2018
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The geodesics in Liouville quantum gravity are not Schramm-Loewner evolutions
J. Miller and W. Qian · 2018
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The distribution of Gaussian multiplicative chaos on the unit interval
G. Remy and T. Zhu · 2018
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Critical Liouville measure as a limit of subcritical measures
J. Aru, E. Powell, and A. Sepúlveda · 2019
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Liouville first-passage percolation: Subsequential scaling limits at high temperature
J. Ding and A. Dunlap · 2019
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A distance exponent for Liouville quantum gravity
E. Gwynne, N. Holden, and X. Sun · 2019
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Metric gluing of Brownian and 8 / 3 \sqrt{8/3} -Liouville quantum gravity surfaces
E. Gwynne and J. Miller · 2019
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KPZ formulas for the Liouville quantum gravity metric
E. Gwynne and J. Pfeffer · 2019
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Bipolar orientations on planar maps and SLE 12 {\rm SLE}_{12}
R. Kenyon, J. Miller, S. Sheffield, and D. B. Wilson · 2019
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Brownian disks and the Brownian snake
J.-F. Le Gall · 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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E. Gwynne, J. Miller, and S. Sheffield · 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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