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We prove the existence of the local weak limit of the measure obtained by sampling random triangulations of size $n$ decorated by an Ising configuration with a weight proportional to the energy of this configuration.
Ising model on a dynamical planar random lattice: exact solution
V. Kazakov · 1986
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B. Duplantier and S. Sheffield · 2011
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Scaling limits of random planar maps with large faces
J.-F. Le Gall and G. Miermont · 2011
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Ergodic theory on stationary random graphs
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G. Borot, J. Bouttier, and E. Guitter · 2012
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N. Curien, L. Ménard, and G. Miermont · 2013
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O. Gurel-Gurevich and A. Nachmias · 2013
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The scaling limit of random simple triangulations and random simple quadrangulations
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Basic properties of the infinite critical-FK random map
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The perimeter cascade in critical Boltzmann quadrangulations decorated by an O(n) loop model
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The Brownian map is the scaling limit of uniform random plane quadrangulations
G. Miermont · 2013
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The scaling limit of uniform random plane maps, via the ambjørn–budd bijection
J. Bettinelli, E. Jacob, and G. Miermont · 2014
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The Brownian plane
N. Curien and J.-F. Le Gall · 2014
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Random geometry on the sphere
J.-F. Le Gall · 2014
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Aspects of random maps
G. Miermont · 2014
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Percolation on random triangulations and stable looptrees
N. Curien and I. Kortchemski · 2015
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L. Chen, N. Curien, and P. Maillard · 2017
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Scaling limits for the peeling process on random maps
N. Curien and J.-F. Le Gall · 2017
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A mating-of-trees approach to graph distances in random planar maps
E. Gwynne, N. Holden, and X. Sun · 2017
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Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map II: local estimates and empty reduced word exponent
E. Gwynne and X. Sun · 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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T. Budd · 2018
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Critical Ising model on random triangulations of the disk: enumeration and local limits
L. Chen and J. Turunen · 2018
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N. Curien and L. Ménard · 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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The geometry of a critical percolation cluster on the UIPT
M. Gorny, E. Maurel-Segala, and A. Singh · 2018
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Volumes in the Uniform Infinite Planar Triangulation: from skeletons to generating functions
L. Ménard · 2018
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A Boltzmann approach to percolation on random triangulations
O. Bernardi, N. Curien, and G. Miermont · 2019
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First-passage percolation and local modifications of distances in random triangulations
N. Curien and J.-F. Le Gall · 2019
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Mating of trees for random planar maps and Liouville quantum gravity: a survey
E. Gwynne, N. Holden, and X. Sun · 2019
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Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map I: cone times
E. Gwynne, C. Mao, and X. Sun · 2019
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