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We endow the $\sqrt{8/3}$-Liouville quantum gravity sphere with a metric space structure and show that the resulting metric measure space agrees in law with the Brownian map.
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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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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KPZ formulas for the Liouville quantum gravity metric
E. Gwynne and J. Pfeffer · 1905
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The dimension of the boundary of a Liouville quantum gravity metric ball
E. Gwynne · 1909
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A two-dimensional growth process
M. Eden · 1961
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Continuous state branching processes
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A decomposition of Bessel bridges
J. Pitman and M. Yor · 1982
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Fractal structure of 2D-quantum gravity
V. Knizhnik, A. Polyakov, and A. Zamolodchikov · 1988
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Brownian motion and stochastic calculus
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Lévy processes
J. Bertoin · 1996
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Decomposition at the maximum for excursions and bridges of one-dimensional diffusions
J. Pitman and M. Yor · 1996
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A large deviation principle for the Brownian snake
L. Serlet · 1997
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Spatial branching processes, random snakes and partial differential equations
J.-F. Le Gall · 1999
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Continuous martingales and Brownian motion
D. Revuz and M. Yor · 1999
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Growth and percolation on the uniform infinite planar triangulation
O. Angel · 2003
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Introductory lectures on fluctuations of Lévy processes with applications
A. E. Kyprianou · 2006
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KPZ in one dimensional random geometry of multiplicative cascades
I. Benjamini and O. Schramm · 2009
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Another derivation of the geometrical KPZ relations
F. David and M. Bauer · 2009
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Exploration trees and conformal loop ensembles
S. Sheffield · 2009
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Geodesics and metric ball boundaries in Liouville quantum gravity
E. Gwynne, J. Pfeffer, and S. Sheffield · 2010
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C. Garban, R. Rhodes, and V. Vargas · 2016
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Liouville heat kernel: regularity and bounds
P. Maillard, R. Rhodes, V. Vargas, and O. Zeitouni · 2016
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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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Imaginary geometry III: reversibility of SLE κ
J. Miller and S. Sheffield · 2016
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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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KPZ formula for log-infinitely divisible multifractal random measures
R. Rhodes and V. Vargas · 2011
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Conformal loop ensembles: the Markovian characterization and the loop-soup construction
S. Sheffield and W. Werner · 2012
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Gaussian multiplicative chaos and KPZ duality
J. Barral, X. Jin, R. Rhodes, and V. Vargas · 2013
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N. Curien and J.-F. Le Gall · 2014
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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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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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Excursion theory for Brownian motion indexed by the Brownian tree
J.-F. Le Gall and C. Abraham · 2018
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A distance exponent for Liouville quantum gravity
E. Gwynne, N. Holden, and X. Sun · 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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An almost sure KPZ relation for SLE and Brownian motion
E. Gwynne, N. Holden, and J. Miller · 2020
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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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An axiomatic characterization of the Brownian map
J. Miller and S. Sheffield · 2021
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Liouville quantum gravity and the Brownian map III: the conformal structure is determined
J. Miller and S. Sheffield · 2021
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