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There is a simple way to "glue together" a coupled pair of continuum random trees (CRTs) to produce a topological sphere.
Universal tail profile of Gaussian multiplicative chaos
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Confluence of geodesics in Liouville quantum gravity for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
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Planar maps are well labeled trees
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The jackknife estimate of variance
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Quantum geometry of bosonic strings
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Exact critical point and critical exponents of O ( n ) {\rm O}(n) models in two dimensions
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A decomposition of Bessel bridges
J. Pitman and M. Yor · 1982
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Extended scaling relations for the magnetic critical exponents of the Potts model
M. den Nijs · 1983
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Conformal invariance and surface critical behavior
J. L. Cardy · 1984
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Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas
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On the Hausdorff dimension of Brownian cone points
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Sur le chaos multiplicatif
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Interacting particle systems
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Exact critical exponents for two-dimensional dense polymers
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Exact surface and wedge exponents for polymers in two dimensions
B. Duplantier and H. Saleur · 1986
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New exact exponents for two-dimensional self-avoiding walks
H. Saleur · 1986
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Critical exponents of Manhattan Hamiltonian walks in two dimensions, from Potts and O ( n ) {\rm O}(n) models
B. Duplantier · 1987
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Exact critical properties of two-dimensional dense self-avoiding walks
B. Duplantier and H. Saleur · 1987
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Coulomb gas formulation of two-dimensional phase transitions
B. Nienhuis · 1987
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Real and complex analysis
W. Rudin · 1987
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Exact determination of the percolation hull exponent in two dimensions
H. Saleur and B. Duplantier · 1987
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Conformal anomaly and scaling dimensions of the O ( n ) {\rm O}(n) model from an exact solution on the honeycomb lattice
M. T. Batchelor and H. W. J. Blöte · 1988
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Conformal field theories coupled to 2 2 -D gravity in the conformal gauge
F. David · 1988
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Conformal spectra of polymers on a random surface
B. Duplantier and I. Kostov · 1988
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Conformal invariance and intersections of random walks
B. Duplantier and K.-H. Kwon · 1988
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Winding-angle distributions of two-dimensional self-avoiding walks from conformal invariance
B. Duplantier and H. Saleur · 1988
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Fractal structure of 2 2 D-quantum gravity
V. G. Knizhnik, A. M. Polyakov, and A. B. Zamolodchikov · 1988
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Conformal field theory and 2 2 D quantum gravity
J. Distler and H. Kawai · 1989
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Fractals in two dimensions and conformal invariance
B. Duplantier · 1989
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O ( n ) {\rm O}(n) vector model on a planar random lattice: spectrum of anomalous dimensions
I. K. Kostov · 1989
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New critical behavior in d = 0 d=0 large- N N matrix models
S. R. Das, A. Dhar, A. M. Sengupta, and S. R. Wadia · 1990
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Geometrical critical phenomena on a random surface of arbitrary genus
B. Duplantier and I. K. Kostov · 1990
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Notes on quantum Liouville theory and quantum gravity
N. Seiberg · 1990
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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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Brownian motion and stochastic calculus
I. Karatzas and S. E. Shreve · 1991
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Critical percolation in finite geometries
J. L. Cardy · 1992
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World-sheet geometry and baby universes in 2 2 D quantum gravity
S. Jain and S. D. Mathur · 1992
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Loop gas model for open strings
V. A. Kazakov and I. K. Kostov · 1992
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Matrix model perturbed by higher order curvature terms
G. P. Korchemsky · 1992
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The continuum random tree. III
D. Aldous · 1993
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A proposal for strings at D > 1 D>1
L. Alvarez-Gaumé, J. L. F. Barbón, and Č. Crnković · 1993
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Exact solution and surface critical behaviour of an O ( n ) {\rm O}(n) model on the honeycomb lattice
M. T. Batchelor and J. Suzuki · 1993
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Lectures on 2D gravity and 2D string theory (TASI 1992)
P. Ginsparg and G. Moore · 1993
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A solvable 2 2 D gravity model with γ > 0 \gamma>0
J. Ambjørn, B. Durhuus, and T. Jónsson · 1994
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Multi-spin systems on a randomly triangulated surface
B. Durhuus · 1994
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2 2 D gravity and random matrices
P. Di Francesco, P. Ginsparg, and J. Zinn-Justin · 1995
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Touching random surfaces and Liouville gravity
I. R. Klebanov · 1995
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Non-perturbative solution of matrix models modified by trace-squared terms
I. R. Klebanov and A. Hashimoto · 1995
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Wormholes, matrix models, and Liouville gravity
I. R. Klebanov and A. Hashimoto · 1995
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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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Random walks and quantum gravity in two dimensions
B. Duplantier · 1998
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Path-crossing exponents and the external perimeter in 2d percolation
M. Aizenman, B. Duplantier, and A. Aharony · 1999
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Subordinators: examples and applications
J. Bertoin · 1999
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Harmonic measure exponents for two-dimensional percolation
B. Duplantier · 1999
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Intersection exponents for planar Brownian motion
G. F. Lawler and W. Werner · 1999
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Continuous martingales and Brownian motion
D. Revuz and M. Yor · 1999
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Conformally invariant fractals and potential theory
B. Duplantier · 2000
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Removability theorems for Sobolev functions and quasiconformal maps
P. W. Jones and S. K. Smirnov · 2000
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Universality for conformally invariant intersection exponents
G. F. Lawler and W. Werner · 2000
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Scaling limits of loop-erased random walks and uniform spanning trees
O. Schramm · 2000
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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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N. Curien and I. Kortchemski · 2014
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N. Curien and J.-F. Le Gall · 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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The dimension of the planar Brownian frontier is 4 / 3 4/3
G. F. Lawler, O. Schramm, and W. Werner · 2001
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Values of Brownian intersection exponents. I. Half-plane exponents
G. F. Lawler, O. Schramm, and W. Werner · 2001
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Values of Brownian intersection exponents. II. Plane exponents
G. F. Lawler, O. Schramm, and W. Werner · 2001
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Mating Siegel quadratic polynomials
M. Yampolsky and S. Zakeri · 2001
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Random trees, Lévy processes and spatial branching processes
T. Duquesne and J.-F. Le Gall · 2002
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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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J.-F. Le Gall · 2014
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Percolations on random maps I: Half-plane models
O. Angel and N. Curien · 2015
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Classification of half-planar maps
O. Angel and G. Ray · 2015
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KPZ relation does not hold for the level lines and SLE κ
J. Aru · 2015
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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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Scaling limits for the critical Fortuin-Kastelyn model on a random planar map III: finite volume case
E. Gwynne and X. Sun · 2015
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Minkowski content of the intersection of a Schramm-Loewner evolution (SLE) curve with the real line
G. F. Lawler · 2015
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Minkowski content and natural parameterization for the Schramm-Loewner evolution
G. F. Lawler and M. A. Rezaei · 2015
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An axiomatic characterization of the Brownian map
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KPZ formula derived from Liouville heat kernel
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The hull process of the Brownian plane
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Liouville quantum gravity on the Riemann sphere
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Convergence of the topology of critical Fortuin-Kasteleyn planar maps to that of CLE κ
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Convergence of loop-erased random walk in the natural parametrization
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Imaginary geometry I: interacting SLEs
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Imaginary geometry III: reversibility of SLE κ
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Liouville quantum gravity and the Brownian map II: geodesics and continuity of the embedding
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Liouville quantum gravity and the Brownian map III: the conformal structure is determined
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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
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Field-measure correspondence in Liouville quantum gravity almost surely commutes with all conformal maps simultaneously
S. Sheffield and M. Wang · 2016
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Two Perspectives of the 2D Unit Area Quantum Sphere and Their Equivalence
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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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Random walk on random planar maps: spectral dimension, resistance, and displacement
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The Tutte embedding of the mated-CRT map converges to Liouville quantum gravity
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Schnyder woods, SLE(16), and Liouville quantum gravity
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Intersections of SLE paths: the double and cut point dimension of SLE
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Natural parametrization of SLE: the Gaussian free field point of view
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Natural parametrization of percolation interface and pivotal points
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SLE as a mating of trees in Euclidean geometry
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Uniqueness of the welding problem for SLE and Liouville quantum gravity
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Tightness of Liouville first passage percolation for γ ∈ ( 0 , 2 ) \gamma\in(0,2)
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