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Liouville quantum gravity (LQG) surfaces are a family of random fractal surfaces which can be thought of as the canonical models of random two-dimensional Riemannian manifolds, in the same sense that Brownian motion is the canonical model of a random path.
External diffusion limited aggregation on a spanning-tree-weighted random planar map
E. Gwynne and J. Pfeffer · 1901
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Bounds for distances and geodesic dimension in Liouville first passage percolation
E. Gwynne and J. Pfeffer · 1903
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Comparison of discrete and continuum Liouville first passage percolation
M. Ang · 1904
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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 · 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
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Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense
E. Gwynne, N. Holden, and X. Sun · 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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Local metrics of the Gaussian free field
E. Gwynne and J. Miller · 1905
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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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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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Convergence of uniform triangulations under the Cardy embedding
N. Holden and X. Sun · 1905
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Precision measurements of Hausdorff dimensions in two-dimensional quantum gravity
J. Barkley and T. Budd · 1908
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L. Lioni and J.-F. Marckert · 1908
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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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An elementary proof of the existence of isothermal parameters on a surface
S.-s. Chern · 1955
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On the enumeration of tree-rooted maps
R. C. Mullin · 1967
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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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Analytic study of fractal structure of quantized surface in two-dimensional quantum gravity
Y. Watabiki · 1992
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Bijective census and random generation of Eulerian planar maps with prescribed vertex degrees
G. Schaeffer · 1997
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Scaling limits of loop-erased random walks and uniform spanning trees
O. Schramm · 2000
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Growth and percolation on the uniform infinite planar triangulation
O. Angel · 2003
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Planar maps as labeled mobiles
J. Bouttier, P. Di Francesco, and E. Guitter · 2004
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Random planar curves and Schramm-Loewner evolutions
W. Werner · 2004
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Conformally invariant processes in the plane
G. F. Lawler · 2005
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Bijective counting of Kreweras walks and loopless triangulations
O. Bernardi · 2007
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Bijective counting of tree-rooted maps and shuffles of parenthesis systems
O. Bernardi · 2007
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Gaussian free fields for mathematicians
S. Sheffield · 2007
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A rigorous perspective on Liouville quantum gravity and the KPZ relation
Liouville quantum gravity and the Brownian map II: geodesics and continuity of the embedding
J. Miller and S. Sheffield · 2016
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Liouville quantum gravity and the Brownian map III: the conformal structure is determined
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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Gaussian multiplicative chaos through the lens of the 2D Gaussian free field
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B. Duplantier · 2010
Cited alongside, same era.
Thick points of the Gaussian free field
X. Hu, J. Miller, and Y. Peres · 2010
Cited alongside, same era.
Liouville quantum gravity and KPZ
B. Duplantier and S. Sheffield · 2011
Cited alongside, same era.
Gaussian multiplicative chaos and KPZ duality
J. Barral, X. Jin, R. Rhodes, and V. Vargas · 2013
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.
J. Aru · 2017
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An elementary approach to Gaussian multiplicative chaos
N. Berestycki · 2017
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Random walk on random planar maps: spectral dimension, resistance, and displacement
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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Lecture notes on Liouville theory and the DOZZ formula
V. Vargas · 2017
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Percolation on triangulations: a bijective path to Liouville quantum gravity
O. Bernardi, N. Holden, and X. Sun · 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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Anomalous diffusion of random walk on random planar maps
E. Gwynne and T. Hutchcroft · 2018
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Upper bounds on Liouville first-passage percolation and Watabiki’s prediction
J. Ding and S. Goswami · 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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Polyakov’s formulation of 2 d 2d bosonic string theory
C. Guillarmou, R. Rhodes, and V. Vargas · 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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A mating-of-trees approach for graph distances in random planar maps
E. Gwynne, N. Holden, and X. Sun · 2020
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E. Gwynne, J. Miller, and S. Sheffield · 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 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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