@misc{GwynneMillerSLECharacterization,
  author = {Gwynne, Ewain and Miller, Jason},
  title = {Characterizations of {SLE}$_\kappa$ for $\kappa\in(4,8)$ on {Liouville} quantum gravity},
  year = {2021},
  howpublished = {arXiv:1701.05174v4},
  eprint = {1701.05174v4},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1701.05174v4},
  note = {Version of 10 February 2021}
}

@misc{SheffieldInventory,
  author = {Sheffield, Scott},
  title = {Quantum gravity and inventory accumulation},
  year = {2015},
  howpublished = {arXiv:1108.2241v2},
  eprint = {1108.2241v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1108.2241v2},
  note = {Version of 23 September 2015}
}

@article{GwynneMaoSunFKI,
  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},
  year = {2019},
  journal = {Annales de l'Institut Henri Poincar\'e, Probabilit\'es et Statistiques},
  volume = {55},
  number = {1},
  pages = {1--60},
  eprint = {1502.00546v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1502.00546v3},
  note = {Version cited: arXiv:1502.00546v3 (8 August 2016)}
}

@article{GwynneSunFKII,
  author = {Gwynne, Ewain and Sun, Xin},
  title = {Scaling limits for the critical {Fortuin--Kastelyn} model on a random planar map {II}: local estimates and empty reduced word exponent},
  year = {2017},
  journal = {Electronic Journal of Probability},
  volume = {22},
  number = {45},
  pages = {1--56},
  eprint = {1505.03375v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1505.03375v3},
  note = {Version cited: arXiv:1505.03375v3 (8 May 2017)}
}

@misc{GwynneSunFKIII,
  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},
  howpublished = {arXiv:1510.06346v1},
  eprint = {1510.06346v1},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1510.06346v1},
  note = {Version of 21 October 2015}
}

@article{DMSMating,
  author = {Duplantier, Bertrand and Miller, Jason and Sheffield, Scott},
  title = {{Liouville} quantum gravity as a mating of trees},
  year = {2021},
  journal = {Ast\'erisque},
  volume = {427},
  doi = {10.24033/ast.1149},
  eprint = {1409.7055v4},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1409.7055v4},
  note = {Version cited: arXiv:1409.7055v4 (18 August 2020)}
}

@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},
  year = {2019},
  volume = {55},
  number = {3},
  pages = {1712--1750},
  doi = {10.1214/18-AIHP932},
  eprint = {1506.03804v4},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1506.03804v4},
  note = {Version cited: arXiv:1506.03804v4 (10 October 2018)}
}

@article{AruHuangSunSphere,
  author = {Aru, Juhan and Huang, Yichao and Sun, Xin},
  title = {Two perspectives of the {2D} unit area quantum sphere and their equivalence},
  year = {2017},
  journal = {Communications in Mathematical Physics},
  volume = {356},
  number = {1},
  pages = {261--283},
  doi = {10.1007/s00220-017-2979-6},
  eprint = {1512.06190v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1512.06190v3},
  note = {Version cited: arXiv:1512.06190v3 (9 September 2017)}
}

@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},
  year = {2026},
  volume = {28},
  number = {11},
  pages = {4893--4949},
  doi = {10.4171/JEMS/1646},
  eprint = {2207.02319v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2207.02319v3},
  note = {Version cited: arXiv:2207.02319v3 (25 March 2025)}
}

@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},
  year = {2017},
  volume = {169},
  pages = {729--869},
  doi = {10.1007/s00440-017-0780-2},
  eprint = {1302.4738v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1302.4738v2},
  note = {Version cited: arXiv:1302.4738v2 (6 April 2017)}
}

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

@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},
  year = {2026},
  volume = {194},
  pages = {1787--1847},
  doi = {10.1007/s00440-025-01430-4},
  eprint = {2406.08674v1},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2406.08674v1},
  note = {Version cited: arXiv:2406.08674v1 (12 June 2024)}
}

@article{GwynneMillerMetric,
  author = {Gwynne, Ewain and Miller, Jason},
  title = {Existence and uniqueness of the {Liouville} quantum gravity metric for $\gamma\in(0,2)$},
  year = {2021},
  journal = {Inventiones Mathematicae},
  volume = {223},
  pages = {213--333},
  doi = {10.1007/s00222-020-00991-6},
  eprint = {1905.00383v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1905.00383v3},
  note = {Version cited: arXiv:1905.00383v3 (22 July 2020)}
}

@misc{GwynneMillerCovariance,
  author = {Gwynne, Ewain and Miller, Jason},
  title = {Conformal covariance of the {Liouville} quantum gravity metric for $\gamma\in(0,2)$},
  year = {2020},
  howpublished = {arXiv:1905.00384v2},
  eprint = {1905.00384v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1905.00384v2},
  note = {Version of 9 September 2020}
}

@article{DubedatEtAlWeakMetric,
  author = {Dub{\'e}dat, 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},
  pages = {369--436},
  year = {2020},
  doi = {10.1007/s00440-020-00979-6},
  eprint = {1905.00380v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1905.00380v2},
  note = {Version cited: 2 June 2020; Lemma 3.20, p. 46; Definition 3.7, p. 32; Proposition 3.14, p. 38}
}

@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},
  year = {2020},
  pages = {677--709},
  doi = {10.1007/s00440-019-00949-7},
  eprint = {1812.03913v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1812.03913v2},
  note = {Theorem locators refer to arXiv:1812.03913v2 (16 October 2019)}
}

@misc{BhatiaKavvadiasConfluence,
  author = {Bhatia, Manan and Kavvadias, Konstantinos},
  title = {Strong confluence of geodesics in {Liouville} quantum gravity},
  year = {2026},
  howpublished = {arXiv:2512.09219v2},
  eprint = {2512.09219v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2512.09219v2},
  note = {Version of 24 August 2026}
}

@misc{IvriiMarkovic2019,
  author = {Ivrii, Oleg and Markovi{\'c}, Vladimir},
  title = {Homogenization of random quasiconformal mappings and random {Delauney} triangulations},
  year = {2019},
  eprint = {1905.07932v1},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1905.07932v1},
  note = {Version cited: 20 May 2019; Lemma 3.1 and equations (3.3)--(3.7), p. 8. Published in Journal of Differential Geometry 124 (2023), 523--551, DOI 10.4310/jdg/1689262063}
}

@article{GwynneMillerQianCLE,
  author = {Gwynne, Ewain and Miller, Jason and Qian, Wei},
  title = {Conformal invariance of {CLE}$_\kappa$ on the {Riemann} sphere for $\kappa\in(4,8)$},
  journal = {International Mathematics Research Notices},
  year = {2021},
  volume = {2021},
  number = {23},
  pages = {17971--18036},
  doi = {10.1093/imrn/rnz328},
  eprint = {1811.00514v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1811.00514v2},
  note = {Version cited: arXiv:1811.00514v2 (8 November 2019)}
}

@misc{MillerWuIntersections,
  author = {Miller, Jason and Wu, Hao},
  title = {Intersections of {SLE} paths: the double and cut point dimension of {SLE}},
  year = {2013},
  howpublished = {arXiv:1303.4725v1},
  eprint = {1303.4725v1},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1303.4725v1},
  note = {Version of 19 March 2013}
}

@article{YuanLoewnerTraces,
  author = {Yuan, Yizheng},
  title = {Topological characterisations of {Loewner} traces},
  year = {2022},
  journal = {Indiana University Mathematics Journal},
  volume = {71},
  number = {3},
  pages = {1027--1046},
  doi = {10.1512/iumj.2022.71.8966},
  eprint = {2003.05535v4},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2003.05535v4},
  note = {Version cited: arXiv:2003.05535v4 (3 July 2022)}
}

@article{SchrammWilsonCoordinateChanges,
  author = {Schramm, Oded and Wilson, David B.},
  title = {{SLE} coordinate changes},
  year = {2005},
  journal = {New York Journal of Mathematics},
  volume = {11},
  pages = {659--669},
  eprint = {math/0505368v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0505368v3},
  note = {Version cited: arXiv:math/0505368v3 (6 April 2006)}
}

@misc{AruHoldenPowellSunCritical,
  author = {Aru, Juhan and Holden, Nina and Powell, Ellen and Sun, Xin},
  title = {{Brownian} half-plane excursion and critical {Liouville} quantum gravity},
  year = {2022},
  howpublished = {arXiv:2109.00275v2},
  eprint = {2109.00275v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/2109.00275v2.pdf},
  note = {Version 2 of 31 August 2022; title as printed in the cited PDF}
}

@misc{GHS-survey,
  author = {Gwynne, Ewain and Holden, Nina and Sun, Xin},
  title = {Mating of trees for random planar maps and {Liouville} quantum gravity: a survey},
  year = {2023},
  howpublished = {arXiv:1910.04713v2},
  eprint = {1910.04713v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1910.04713v2},
  note = {Version of 15 February 2023}
}

@article{HS-Cardy,
  author = {Holden, Nina and Sun, Xin},
  title = {Convergence of uniform triangulations under the {Cardy} embedding},
  year = {2023},
  journal = {Acta Mathematica},
  volume = {230},
  number = {1},
  pages = {93--203},
  doi = {10.4310/ACTA.2023.v230.n1.a2},
  eprint = {1905.13207v3},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/1905.13207v3},
  note = {Version cited: arXiv:1905.13207v3 (2 June 2021)}
}

@misc{HS-survey,
  author = {Holden, Nina and Sun, Xin},
  title = {{Liouville} quantum gravity: from random planar maps to conformal field theory},
  year = {2025},
  howpublished = {arXiv:2510.16431v1},
  eprint = {2510.16431v1},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2510.16431v1},
  note = {Version of 18 October 2025}
}

@article{Whitney1932,
  author = {Whitney, Hassler},
  title = {Congruent graphs and the connectivity of graphs},
  journal = {American Journal of Mathematics},
  year = {1932},
  volume = {54},
  number = {1},
  pages = {150--168},
  doi = {10.2307/2371086},
  url = {https://www.jstor.org/stable/2371086}
}

@misc{Intrinsic-input,
  author = {{OpenAI}},
  title = {{Metric-measure limits of subcritical FK and spanning-tree planar maps}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026/main.pdf}{OAI:Metric-measure-limits-of-subcritical-FK-and-spanning-tree-planar-maps-September-24-2026}},
  year = {2026},
  note = {Theorem~1.1, fixed-$q$ FK clause}
}

@article{MillerWatsonWilsonNestingField,
  author = {Miller, Jason and Watson, Samuel S. and Wilson, David B.},
  title = {The conformal loop ensemble nesting field},
  journal = {Probability Theory and Related Fields},
  volume = {163},
  number = {3},
  pages = {769--801},
  year = {2015},
  doi = {10.1007/s00440-014-0604-6},
  eprint = {1401.0218v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/pdf/1401.0218v2},
  note = {Cited version: arXiv:1401.0218v2, 21 December 2014}
}

@incollection{AhlforsBeurling1952ConformalInvariants,
  author = {Ahlfors, Lars V. and Beurling, Arne},
  title = {Conformal invariants},
  editor = {Beckenbach, Edwin F.},
  booktitle = {Construction and Applications of Conformal Maps},
  series = {National Bureau of Standards Applied Mathematics Series},
  volume = {18},
  chapter = {27},
  pages = {243--245},
  publisher = {U.S. Government Printing Office},
  address = {Washington, D.C.},
  year = {1952},
  url = {https://digital.library.unt.edu/ark:/67531/metadc40298/m2/1/high_res_d/applmathser_18_w.pdf},
  note = {Volume issued 26 December 1952; proceedings of a symposium held 22--25 June 1949}
}

@book{AstalaIwaniecMartin2009,
  author = {Astala, Kari and Iwaniec, Tadeusz and Martin, Gaven},
  title = {Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane},
  series = {Princeton Mathematical Series},
  volume = {48},
  publisher = {Princeton University Press},
  address = {Princeton, NJ},
  year = {2009},
  isbn = {9780691137773},
  doi = {10.1515/9781400830114},
  url = {https://api.pageplace.de/preview/DT0400.9781400830114_A25083002/preview-9781400830114_A25083002.pdf}
}

@article{Cristea1989Quasiconformality,
  author = {Cristea, Mihai},
  title = {Some conditions for quasiconformality},
  journal = {Annales Academiae Scientiarum Fennicae. Series A I. Mathematica},
  volume = {14},
  pages = {345--350},
  year = {1989},
  doi = {10.5186/aasfm.1989.1405},
  url = {https://www.acadsci.fi/mathematica/Vol14/vol14pp345-350.pdf},
  note = {Theorem 1, p. 348; supporting Lemmas 1--2, pp. 346--347}
}

@book{SaintGervais2016Uniformization,
  author = {{Henri Paul de Saint-Gervais}},
  title = {Uniformization of {Riemann} Surfaces: Revisiting a Hundred-Year-Old Theorem},
  translator = {Burns, Robert G.},
  series = {Heritage of European Mathematics},
  publisher = {European Mathematical Society},
  address = {Z{\"u}rich},
  year = {2016},
  isbn = {9783037191453},
  doi = {10.4171/145},
  url = {https://ems.press/books/hem/222},
  note = {Theorem II.2.15, p. 61; genus-zero proof from Riemann--Roch. Collective author}
}

@misc{HoldenYuUniformization,
  author = {Holden, Nina and Yu, Pu},
  title = {Circle packing and {Riemann} uniformization of random planar maps in an ergodic scale-free environment},
  year = {2026},
  howpublished = {arXiv:2603.06528v2},
  eprint = {2603.06528v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2603.06528v2},
  note = {Version of 6 May 2026}
}

@article{DoneyBivariate,
  author = {Doney, R. A.},
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}

@article{GwynneMillerSheffieldTutte,
  author = {Gwynne, Ewain and Miller, Jason and Sheffield, Scott},
  title = {The {Tutte} embedding of the mated-{CRT} map converges to {Liouville} quantum gravity},
  journal = {The Annals of Probability},
  volume = {49},
  number = {4},
  year = {2021},
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  doi = {10.1214/20-AOP1487},
  eprint = {1705.11161v5},
  archivePrefix = {arXiv},
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  note = {Version consulted: arXiv:1705.11161v5 (20 February 2021)}
}

@article{DingDubedatDunlapFalconetTightness,
  author = {Ding, Jian and Dub\'edat, Julien and Dunlap, Alexander and Falconet, Hugo},
  title = {Tightness of {Liouville} first passage percolation for $\gamma\in(0,2)$},
  journal = {Publications Math\'ematiques de l'IH\'ES},
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  url = {https://www.numdam.org/articles/10.1007/s10240-020-00121-1/}
}

@article{SheffieldExplorationTrees,
  author = {Sheffield, Scott},
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  journal = {Duke Mathematical Journal},
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  doi = {10.1215/00127094-2009-007},
  eprint = {math/0609167v2},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0609167v2},
  note = {Version consulted: arXiv:math/0609167v2 (23 November 2006)}
}

@article{FortuinKasteleyn1972,
  author = {Fortuin, C. M. and Kasteleyn, P. W.},
  title = {On the random-cluster model. {I}. {Introduction} and relation to other models},
  journal = {Physica},
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  number = {4},
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  year = {1972},
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}

@article{Mullin1967,
  author = {Mullin, R. C.},
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  year = {1967},
  doi = {10.4153/CJM-1967-010-x},
  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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}

@article{DuplantierSheffieldKPZ2011,
  author = {Duplantier, Bertrand and Sheffield, Scott},
  title = {Liouville quantum gravity and {KPZ}},
  journal = {Inventiones Mathematicae},
  volume = {185},
  number = {2},
  pages = {333--393},
  year = {2011},
  doi = {10.1007/s00222-010-0308-1},
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}

@article{Bernardi2008Subgraphs,
  author = {Bernardi, Olivier},
  title = {{Tutte} polynomial, subgraphs, orientations and sandpile model:
           new connections via embeddings},
  journal = {The Electronic Journal of Combinatorics},
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  number = {1},
  pages = {Research Paper R109},
  year = {2008},
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  eprint = {math/0612003v1},
  archivePrefix = {arXiv},
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  note = {Section locators refer to arXiv:math/0612003v1}
}

@article{KahaneChaos1985,
  author = {Kahane, Jean-Pierre},
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}

@article{DKRVSphere2016,
  author = {David, Fran\c{c}ois and Kupiainen, Antti and
            Rhodes, R\'emi and Vargas, Vincent},
  title = {{Liouville} quantum gravity on the {Riemann} sphere},
  journal = {Communications in Mathematical Physics},
  volume = {342},
  number = {3},
  pages = {869--907},
  year = {2016},
  doi = {10.1007/s00220-016-2572-4},
  eprint = {1410.7318v4},
  archivePrefix = {arXiv},
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  note = {Version cited: arXiv:1410.7318v4 (5 June 2015)}
}