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We prove a scaling limit result for random walk on certain random planar maps with its natural time parametrization.
Liouville quantum gravity surfaces with boundary as matings of trees
M. Ang and E. Gwynne · 1903
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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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How to draw a graph
W. T. Tutte · 1963
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On the enumeration of tree-rooted maps
R. C. Mullin · 1967
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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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Conformal field theories coupled to 2-D gravity in the conformal gauge
F. David · 1988
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Conformal field theory and 2D quantum gravity
J. Distler and H. Kawai · 1989
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Boundary behaviour of conformal maps
C. Pommerenke · 1992
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Generating random spanning trees more quickly than the cover time
D. B. Wilson · 1996
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The spectral dimension of 2d quantum gravity
J. Ambjørn, J. L. Nielsen, J. Rolf, D. Boulatov, and Y. Watabiki · 1998
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Quantum geometry and diffusion
J. Ambjørn, K. N. Anagnostopoulos, L. Jensen, T. Ichihara, and Y. Watabiki · 1999
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Hölder regularity and dimension bounds for random curves
M. Aizenman and A. Burchard · 1999
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Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
A. Grigor’yan · 1999
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Continuous martingales and Brownian motion
D. Revuz and M. Yor · 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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Random walks with strongly inhomogeneous rates and singular diffusions: convergence, localization and aging in one dimension
L. R. G. Fontes, M. Isopi, and C. M. Newman · 2002
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Foundations of modern probability
O. Kallenberg · 2002
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Uniform infinite planar triangulations
O. Angel and O. Schramm · 2003
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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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Basic properties of SLE
S. Rohde and O. Schramm · 2005
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Scaling limit for trap models on ℤ d \mathbb{Z}^{d}
G. Ben Arous and J. Černỳ · 2007
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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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Markov chains and mixing times
D. A. Levin, Y. Peres, and E. L. Wilmer · 2009
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Liouville quantum gravity and KPZ
B. Duplantier and S. Sheffield · 2011
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Dirichlet forms and symmetric Markov processes
M. Fukushima, Y. Oshima, and M. Takeda · 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
J. Miller and S. Sheffield · 2016
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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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S. Sheffield and M. Wang · 2016
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I. Benjamini and N. Curien · 2013
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Convergence of probability measures
P. Billingsley · 2013
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Recurrence of planar graph limits
O. Gurel-Gurevich and A. Nachmias · 2013
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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
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A contour line of the continuum Gaussian free field
O. Schramm and S. Sheffield · 2013
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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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N. Berestycki · 2017
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Time-changes of stochastic processes associated with resistance forms
D. Croydon, B. Hambly, and T. Kumagai · 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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An invariance principle for ergodic scale-free random environments
E. Gwynne, J. Miller, and S. Sheffield · 2018
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Liouville Brownian motion and thick points of the Gaussian free field
H. Jackson · 2018
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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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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 S L E 12 {\mathrm{S}LE}_{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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Anomalous diffusion of random walk on random planar maps
E. Gwynne and T. Hutchcroft · 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 and J. Pfeffer · 2020
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Planar Maps, Random Walks and Circle Packing: École D’Été de Probabilités de Saint-Flour XLVIII-2018
A. Nachmias · 2020
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Liouville quantum gravity as a mating of trees
B. Duplantier, J. Miller, and S. Sheffield · 2021
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Random walk on random planar maps: Spectral dimension, resistance and displacement
E. Gwynne and J. Miller · 2021
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The Tutte embedding of the mated-crt map converges to Liouville quantum gravity
E. Gwynne, J. Miller, and S. Sheffield · 2021
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