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We prove that the Tutte embeddings (a.k.a.
External diffusion limited aggregation on a spanning-tree-weighted random planar map
E. Gwynne and J. Pfeffer · 1901
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Liouville quantum gravity surfaces with boundary as matings of trees
M. Ang and E. Gwynne · 1903
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A combinatorial criterion for macroscopic circles in planar triangulations
O. Gurel-Gurevich, D. C. Jerison, and A. Nachmias · 1906
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Concerning upper semi-continuous collections of continua
R. L. Moore · 1928
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The dissection of rectangles into squares
R. L. Brooks, C. A. B. Smith, A. H. Stone, W. T. Tutte, et al · 1940
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On the enumeration of tree-rooted maps
R. C. Mullin · 1967
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An approximation of partial sums of independent RV’s, and the sample DF. II
J. Komlós, P. Major, and G. Tusnády · 1976
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Sur le chaos multiplicatif
J.-P. Kahane · 1985
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Excursions in a cone for two-dimensional Brownian motion
M. Shimura · 1985
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The continuum random tree. I
D. Aldous · 1991
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The continuum random tree. II. An overview
D. Aldous · 1991
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The continuum random tree. III
D. Aldous · 1993
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Square tilings with prescribed combinatorics
O. Schramm · 1993
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The combinatorial Riemann mapping theorem
J. W. Cannon · 1994
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Random walks of circle packings
T. Dubejko · 1995
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Multidimensional version of the results of Komlós, Major and Tusnády for vectors with finite exponential moments
A. Y. Zaitsev · 1998
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Hölder regularity and dimension bounds for random curves
M. Aizenman and A. Burchard · 1999
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Scaling limits of loop-erased random walks and uniform spanning trees
O. Schramm · 2000
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Recurrence of distributional limits of finite planar graphs
I. Benjamini and O. Schramm · 2001
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Critical percolation in the plane: conformal invariance, Cardy’s formula, scaling limits
S. Smirnov · 2001
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Random walks on mated-CRT planar maps and Liouville Brownian motion
N. Berestycki and E. Gwynne · 2003
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Circle packing: a mathematical tale
K. Stephenson · 2003
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Liouville field theory: a decade after the revolution
Y. Nakayama · 2004
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Basic properties of SLE
S. Rohde and O. Schramm · 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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Contour lines of the two-dimensional discrete Gaussian free field
O. Schramm and S. Sheffield · 2009
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Recent progress on the random conductance model
M. Biskup · 2011
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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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Simple random walk on the uniform infinite planar quadrangulation: subdiffusivity via pioneer points
I. Benjamini and N. Curien · 2013
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Recurrence of planar graph limits
O. Gurel-Gurevich and A. Nachmias · 2013
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On the Riemann surface type of random planar maps
J. T. Gill and S. Rohde · 2013
Brownian motion correlation in the peanosphere for κ > 8 \kappa>8
E. Gwynne, N. Holden, J. Miller, and X. Sun · 2017
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E. Gwynne and J. Miller · 2017
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Convergence of percolation on uniform quadrangulations with boundary to SLE 6
E. Gwynne and J. Miller · 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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Conformal growth rates and spectral geometry on distributional limits of graphs
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Uniqueness and universality of the Brownian map
J.-F. Le Gall · 2013
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The Brownian map is the scaling limit of uniform random plane quadrangulations
G. Miermont · 2013
Cited alongside, same era.
A contour line of the continuum Gaussian free field
O. Schramm and S. Sheffield · 2013
Cited alongside, same era.
Liouville quantum gravity as a mating of trees
B. Duplantier, J. Miller, and S. Sheffield · 2014
Cited alongside, same era.
Gaussian multiplicative chaos and applications: A review
R. Rhodes and V. Vargas · 2014
Cited alongside, same era.
Diffusion in planar Liouville quantum gravity
N. Berestycki · 2015
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A glimpse of the conformal structure of random planar maps
N. Curien · 2015
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J. R. Lee · 2017
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Schnyder woods, SLE(16), and Liouville quantum gravity
Y. Li, X. Sun, and S. S. Watson · 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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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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Negative moments for Gaussian multiplicative chaos on fractal sets
C. Garban, N. Holden, A. Sepúlveda, and X. Sun · 2018
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E. Gwynne, A. Kassel, J. Miller, and D. B. Wilson · 2018
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An invariance principle for ergodic scale-free random environments
E. Gwynne, J. Miller, and S. Sheffield · 2018
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Minkowski content of Brownian cut points
N. Holden, G. F. Lawler, X. Li, and X. Sun · 2018
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Natural parametrization of percolation interface and pivotal points
N. Holden, X. Li, and X. Sun · 2018
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Liouville quantum gravity on the unit disk
Y. Huang, R. Rhodes, and V. Vargas · 2018
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SLE as a mating of trees in Euclidean geometry
N. Holden and X. Sun · 2018
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Discrete Uniformizing Metrics on Distributional Limits of Sphere Packings
J. R. Lee · 2018
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A distance exponent for Liouville quantum gravity
E. Gwynne, N. Holden, and X. Sun · 2019
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Harmonic functions on mated-CRT maps
E. Gwynne, J. Miller, and S. Sheffield · 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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Liouville quantum gravity spheres as matings of finite-diameter trees
J. Miller and S. Sheffield · 2019
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Return probability and recurrence for the random walk driven by two-dimensional Gaussian free field
M. Biskup, J. Ding, and S. Goswami · 2020
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Every planar graph with the Liouville property is amenable
J. Carmesin and A. Georgakopoulos · 2020
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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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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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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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