@article{BorgaGwynneSunPermutons,
  author = {Borga, Jacopo and Gwynne, Ewain and Sun, Xin},
  title = {Permutons, meanders, and {SLE}-decorated {Liouville} quantum gravity},
  journal = {Journal of the European Mathematical Society},
  volume = {28},
  number = {11},
  pages = {4893--4949},
  year = {2026},
  doi = {10.4171/JEMS/1646},
  eprint = {2207.02319},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/2207.02319v3},
  note = {\href{https://arxiv.org/abs/2207.02319v3}{arXiv:2207.02319v3}}
}

@article{AruHuangSunSphere,
  author = {Aru, Juhan and Huang, Yichao and Sun, Xin},
  title = {Two perspectives of the {2D} unit area quantum sphere and their equivalence},
  journal = {Communications in Mathematical Physics},
  volume = {356},
  number = {1},
  pages = {261--283},
  year = {2017},
  doi = {10.1007/s00220-017-2979-6},
  eprint = {1512.06190},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1512.06190v3},
  note = {\href{https://arxiv.org/abs/1512.06190v3}{arXiv:1512.06190v3}}
}

@article{SheffieldQuantumZipper,
  author = {Sheffield, Scott},
  title = {Conformal weldings of random surfaces: {SLE} and the quantum gravity zipper},
  journal = {The Annals of Probability},
  volume = {44},
  number = {5},
  pages = {3474--3545},
  year = {2016},
  doi = {10.1214/15-AOP1055},
  eprint = {1012.4797},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1012.4797v2},
  note = {\href{https://arxiv.org/abs/1012.4797v2}{arXiv:1012.4797v2}}
}

@article{SheffieldInventory,
  author = {Sheffield, Scott},
  title = {Quantum gravity and inventory accumulation},
  journal = {The Annals of Probability},
  volume = {44},
  number = {6},
  pages = {3804--3848},
  year = {2016},
  doi = {10.1214/15-AOP1061},
  eprint = {1108.2241},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1108.2241v2},
  note = {\href{https://arxiv.org/abs/1108.2241v2}{arXiv:1108.2241v2}}
}

@misc{GwynneSunFinite,
  author = {Gwynne, Ewain and Sun, Xin},
  title = {Scaling limits for the critical {Fortuin-Kastelyn} model on a random planar map {III}: finite volume case},
  year = {2015},
  eprint = {1510.06346},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1510.06346v1},
  note = {\href{https://arxiv.org/abs/1510.06346v1}{arXiv:1510.06346v1}}
}

@article{MillerSheffieldSphere,
  author = {Miller, Jason and Sheffield, Scott},
  title = {Liouville quantum gravity spheres as matings of finite-diameter trees},
  journal = {Annales de l'Institut Henri Poincar\'e, Probabilit\'es et Statistiques},
  volume = {55},
  number = {3},
  pages = {1712--1750},
  year = {2019},
  doi = {10.1214/18-AIHP932},
  eprint = {1506.03804},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1506.03804v4},
  note = {\href{https://arxiv.org/abs/1506.03804v4}{arXiv:1506.03804v4}}
}

@book{DMS,
  author = {Duplantier, Bertrand and Miller, Jason and Sheffield, Scott},
  title = {Liouville quantum gravity as a mating of trees},
  series = {Ast\'erisque},
  volume = {427},
  publisher = {Soci\'et\'e Math\'ematique de France},
  year = {2021},
  doi = {10.24033/ast.1149},
  isbn = {978-2-85629-941-8},
  eprint = {1409.7055},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1409.7055v4},
  note = {\href{https://arxiv.org/abs/1409.7055v4}{arXiv:1409.7055v4}}
}

@article{GwynneMillerMetric,
  author = {Gwynne, Ewain and Miller, Jason},
  title = {Existence and uniqueness of the {Liouville} quantum gravity metric for {$\gamma\in(0,2)$}},
  journal = {Inventiones Mathematicae},
  volume = {223},
  number = {1},
  pages = {213--333},
  year = {2021},
  doi = {10.1007/s00222-020-00991-6},
  eprint = {1905.00383},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1905.00383v3},
  note = {\href{https://arxiv.org/abs/1905.00383v3}{arXiv:1905.00383v3}}
}

@article{GwynneMillerLocalMetrics,
  author = {Gwynne, Ewain and Miller, Jason},
  title = {Local metrics of the {Gaussian} free field},
  journal = {Annales de l'Institut Fourier},
  volume = {70},
  number = {5},
  pages = {2049--2075},
  year = {2020},
  doi = {10.5802/aif.3398},
  eprint = {1905.00379},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1905.00379v2},
  note = {\href{https://arxiv.org/abs/1905.00379v2}{arXiv:1905.00379v2}}
}

@misc{GwynnePfefferKPZ,
  author = {Gwynne, Ewain and Pfeffer, Joshua},
  title = {{KPZ} formulas for the {Liouville} quantum gravity metric},
  year = {2019},
  eprint = {1905.11790},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1905.11790v3},
  note = {\href{https://arxiv.org/abs/1905.11790v3}{arXiv:1905.11790v3}}
}

@article{DFGPSWeakMetric,
  author = {Dub\'edat, Julien and Falconet, Hugo and Gwynne, Ewain and Pfeffer, Joshua and Sun, Xin},
  title = {Weak {LQG} metrics and {Liouville} first passage percolation},
  journal = {Probability Theory and Related Fields},
  volume = {178},
  number = {1--2},
  pages = {369--436},
  year = {2020},
  doi = {10.1007/s00440-020-00979-6},
  eprint = {1905.00380},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1905.00380v2},
  note = {\href{https://arxiv.org/abs/1905.00380v2}{arXiv:1905.00380v2}}
}

@article{GwynneMillerConformal,
  author = {Gwynne, Ewain and Miller, Jason},
  title = {Conformal covariance of the {Liouville} quantum gravity metric for {$\gamma\in(0,2)$}},
  journal = {Annales de l'Institut Henri Poincar\'e, Probabilit\'es et Statistiques},
  volume = {57},
  number = {2},
  pages = {1016--1031},
  year = {2021},
  doi = {10.1214/20-AIHP1105},
  eprint = {1905.00384},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1905.00384v2},
  note = {\href{https://arxiv.org/abs/1905.00384v2}{arXiv:1905.00384v2}}
}

@article{BettinelliJacobMiermontUniform,
  author = {Bettinelli, J\'er\'emie and Jacob, Emmanuel and Miermont, Gr\'egory},
  title = {The scaling limit of uniform random plane maps, via the {Ambj{\o}rn--Budd} bijection},
  journal = {Electronic Journal of Probability},
  volume = {19},
  number = {74},
  pages = {1--16},
  year = {2014},
  doi = {10.1214/EJP.v19-3213},
  eprint = {1312.5842},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://bettinel.perso.math.cnrs.fr/papers/14_uniform_maps.pdf},
  note = {\href{https://bettinel.perso.math.cnrs.fr/papers/14_uniform_maps.pdf}{Published version}}
}

@article{MillerSheffieldBrownianII,
  author = {Miller, Jason and Sheffield, Scott},
  title = {{Liouville} quantum gravity and the {Brownian} map {II}: geodesics and continuity of the embedding},
  journal = {The Annals of Probability},
  volume = {49},
  number = {6},
  pages = {2732--2829},
  year = {2021},
  doi = {10.1214/21-AOP1506},
  eprint = {1605.03563},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1605.03563v3},
  note = {\href{https://arxiv.org/abs/1605.03563v3}{arXiv:1605.03563v3}}
}

@article{GwynneHoldenSunGraphDistances,
  author = {Gwynne, Ewain and Holden, Nina and Sun, Xin},
  title = {A mating-of-trees approach for graph distances in random planar maps},
  journal = {Probability Theory and Related Fields},
  volume = {177},
  number = {3--4},
  pages = {1043--1102},
  year = {2020},
  doi = {10.1007/s00440-020-00969-8},
  eprint = {1711.00723},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1711.00723v3},
  note = {\href{https://arxiv.org/abs/1711.00723v3}{arXiv:1711.00723v3}}
}

@article{DingGwynneDimension,
  author = {Ding, Jian and Gwynne, Ewain},
  title = {The fractal dimension of {Liouville} quantum gravity: universality, monotonicity, and bounds},
  journal = {Communications in Mathematical Physics},
  volume = {374},
  pages = {1877--1934},
  year = {2020},
  doi = {10.1007/s00220-019-03487-4},
  eprint = {1807.01072},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1807.01072v3},
  note = {\href{https://arxiv.org/abs/1807.01072v3}{arXiv:1807.01072v3}}
}

@misc{BhatiaKavvadiasConfluence,
  author = {Bhatia, Manan and Kavvadias, Konstantinos},
  title = {Strong confluence of geodesics in {Liouville} quantum gravity},
  year = {2026},
  eprint = {2512.09219},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  doi = {10.48550/arXiv.2512.09219},
  url = {https://arxiv.org/abs/2512.09219v2},
  note = {\href{https://arxiv.org/abs/2512.09219v2}{arXiv:2512.09219v2}}
}

@article{GwynneMillerSheffieldHarmonic,
  author = {Gwynne, Ewain and Miller, Jason and Sheffield, Scott},
  title = {Harmonic functions on mated-{CRT} maps},
  journal = {Electronic Journal of Probability},
  volume = {24},
  number = {58},
  year = {2019},
  pages = {1--55},
  doi = {10.1214/19-EJP325},
  eprint = {1807.07511},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1807.07511v3},
  note = {\href{https://arxiv.org/abs/1807.07511v3}{arXiv:1807.07511v3}}
}

@article{ContrerasHipGwynneCurvature,
  author = {Contreras Hip, Andres A. and Gwynne, Ewain},
  title = {Gaussian curvature on random planar maps and {Liouville} quantum gravity},
  journal = {Probability Theory and Related Fields},
  volume = {194},
  year = {2026},
  pages = {1787--1847},
  doi = {10.1007/s00440-025-01430-4},
  eprint = {2406.08674},
  archivePrefix = {arXiv},
  url = {https://link.springer.com/article/10.1007/s00440-025-01430-4},
  note = {\href{https://doi.org/10.1007/s00440-025-01430-4}{Published version}}
}

@article{GwynneHoldenSunBipolar,
  author = {Gwynne, Ewain and Holden, Nina and Sun, Xin},
  title = {Joint scaling limit of a bipolar-oriented triangulation and its dual in the peanosphere sense},
  journal = {Acta Mathematica Sinica, English Series},
  volume = {42},
  number = {6},
  year = {2026},
  pages = {1509--1554},
  doi = {10.1007/s10114-026-4359-7},
  eprint = {1603.01194},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1603.01194v2},
  note = {\href{https://arxiv.org/abs/1603.01194v2}{arXiv:1603.01194v2}}
}

@article{MillerSheffieldIGIV,
  author = {Miller, Jason and Sheffield, Scott},
  title = {Imaginary geometry {IV}: interior rays, whole-plane reversibility, and space-filling trees},
  journal = {Probability Theory and Related Fields},
  volume = {169},
  number = {3--4},
  year = {2017},
  pages = {729--869},
  doi = {10.1007/s00440-017-0780-2},
  eprint = {1302.4738},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1302.4738v2},
  note = {\href{https://arxiv.org/abs/1302.4738v2}{arXiv:1302.4738v2}}
}

@article{MillerQianGeodesics,
  author = {Miller, Jason and Qian, Wei},
  title = {The geodesics in {Liouville} quantum gravity are not {Schramm--Loewner} evolutions},
  journal = {Probability Theory and Related Fields},
  volume = {177},
  number = {3--4},
  year = {2020},
  pages = {677--709},
  doi = {10.1007/s00440-019-00949-7},
  eprint = {1812.03913},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1812.03913v2},
  note = {\href{https://arxiv.org/abs/1812.03913v2}{arXiv:1812.03913v2}}
}

@misc{TimorinMoore,
  author = {Timorin, Vladlen},
  title = {{Moore}'s theorem},
  year = {2010},
  eprint = {1001.5140},
  archivePrefix = {arXiv},
  primaryClass = {math.DS},
  url = {https://arxiv.org/abs/1001.5140v1},
  note = {\href{https://arxiv.org/abs/1001.5140v1}{arXiv:1001.5140v1}}
}

@article{GwynneMaoSunConeTimes,
  author = {Gwynne, Ewain and Mao, Cheng and Sun, Xin},
  title = {Scaling limits for the critical {Fortuin--Kasteleyn} model on a random planar map {I}: cone times},
  journal = {Annales de l'Institut Henri Poincar\'e, Probabilit\'es et Statistiques},
  volume = {55},
  number = {1},
  pages = {1--60},
  year = {2019},
  doi = {10.1214/17-AIHP874},
  eprint = {1502.00546},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  url = {https://arxiv.org/abs/1502.00546v3},
  note = {\href{https://arxiv.org/abs/1502.00546v3}{arXiv:1502.00546v3}}
}

@incollection{GHSSurvey,
  author    = {Gwynne, Ewain and Holden, Nina and Sun, Xin},
  title     = {{Mating of trees for random planar maps and Liouville quantum gravity: a survey}},
  booktitle = {{Topics in statistical mechanics}},
  editor    = {Boutillier, C\'edric and de Tili\`ere, B\'eatrice and Raschel, Kilian},
  series    = {Panoramas et Synth\`eses},
  volume    = {59},
  pages     = {41--120},
  publisher = {Soci\'et\'e Math\'ematique de France},
  address   = {Paris},
  year      = {2023},
  eprint    = {1910.04713},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  note = {\href{https://arxiv.org/abs/1910.04713v2}{arXiv:1910.04713v2}}
}

@misc{HSSurvey,
  author    = {Holden, Nina and Sun, Xin},
  title     = {{Liouville quantum gravity: from random planar maps to conformal field theory}},
  year      = {2025},
  eprint    = {2510.16431},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  howpublished = {Preprint for the Proceedings of the International Congress of Mathematicians 2026},
  note = {\href{https://arxiv.org/abs/2510.16431v1}{arXiv:2510.16431v1}}
}

@article{DHBijection,
  author = {Duchi, Enrica and Henriet, Corentin},
  title = {A Bijection Between Non-Separable Planar Maps and Fighting Fish},
  journal = {Electronic Journal of Combinatorics},
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  pages = {P2.22},
  year = {2026},
  doi = {10.37236/11653},
  url = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i2p22},
  note = {\href{https://doi.org/10.37236/11653}{Published version}; Section~2.3, Theorem~1}
}

@article{BenoistLength,
  author    = {Benoist, St\'ephane},
  title     = {{Natural parametrization of SLE: the Gaussian free field point of view}},
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  number    = {103},
  pages     = {1--16},
  year      = {2018},
  doi       = {10.1214/18-EJP232},
  eprint    = {1708.03801},
  archivePrefix = {arXiv},
  primaryClass = {math.PR},
  note = {\href{https://arxiv.org/abs/1708.03801v1}{arXiv:1708.03801v1}}
}

@article{MiermontTessellations,
  author = {Miermont, Gr{\'e}gory},
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  note = {\href{https://numdam.org/item/10.24033/asens.2108.pdf}{Published version}}
}

@article{FortuinKasteleyn1972,
  author = {Fortuin, C. M. and Kasteleyn, P. W.},
  title = {On the random-cluster model. {I}. {Introduction} and relation to other models},
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}

@article{Mullin1967,
  author = {Mullin, R. C.},
  title = {On the enumeration of tree-rooted maps},
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  year = {1967},
  doi = {10.4153/CJM-1967-010-x},
  url = {https://doi.org/10.4153/CJM-1967-010-x},
  note = {\url{https://doi.org/10.4153/CJM-1967-010-x}}
}

@article{Bernardi2007,
  author = {Bernardi, Olivier},
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  eprint = {math/0601684},
  archivePrefix = {arXiv},
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  note = {\url{https://arxiv.org/abs/math/0601684v1}}
}

@article{DuplantierSheffieldKPZ2011,
  author = {Duplantier, Bertrand and Sheffield, Scott},
  title = {Liouville quantum gravity and {KPZ}},
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  year = {2011},
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  note = {\url{https://doi.org/10.1007/s00222-010-0308-1}}
}

@article{DDDFLFPPTightness,
  author = {Ding, Jian and Dub{\'e}dat, Julien and Dunlap, Alexander and Falconet, Hugo},
  title = {Tightness of {Liouville} first passage percolation for $\gamma\in(0,2)$},
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  year = {2020},
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  eprint = {1904.08021},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1007/s10240-020-00121-1}}
}

@article{LeGallBrownianMap,
  author = {Le Gall, Jean-Fran{\c c}ois},
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  year = {2013},
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  eprint = {1105.4842},
  archivePrefix = {arXiv},
  note = {\url{https://doi.org/10.1214/12-AOP792}}
}

@article{MiermontBrownianMap,
  author = {Miermont, Gr{\'e}gory},
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  eprint = {1104.1606},
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}

@article{GrevenPfaffelhuberWinter,
  author = {Greven, Andreas and Pfaffelhuber, Peter and Winter, Anita},
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}

@article{AthreyaLohrWinter,
  author = {Athreya, Siva and L{\"o}hr, Wolfgang and Winter, Anita},
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}

@article{GwynnePfefferDLA,
  author = {Gwynne, Ewain and Pfeffer, Joshua},
  title = {External diffusion-limited aggregation on a spanning-tree-weighted random planar map},
  journal = {The Annals of Probability},
  volume = {49},
  number = {4},
  pages = {1633--1676},
  year = {2021},
  doi = {10.1214/20-AOP1486},
  note = {Preprint version: \href{https://arxiv.org/abs/1901.06860v4}{arXiv:1901.06860v4}}
}