@article{HuangYau,
  author = {Huang, Jiaoyang and Yau, Horng-Tzer},
  title = {Spectrum of random {$d$}-regular graphs up to the edge},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {77},
  number = {3},
  pages = {1635--1723},
  year = {2024},
  doi = {10.1002/cpa.22176},
  url = {https://arxiv.org/abs/2102.00963v3},
  note = {Theorem numbering follows arXiv:2102.00963v3, revised 2 February 2025}
}

@article{LandonSosoeYau,
  author = {Landon, Benjamin and Sosoe, Philippe and Yau, Horng-Tzer},
  title = {Fixed energy universality of {Dyson Brownian} motion},
  journal = {Advances in Mathematics},
  volume = {346},
  pages = {1137--1332},
  year = {2019},
  doi = {10.1016/j.aim.2019.02.010},
  url = {https://arxiv.org/abs/1609.09011v3},
  note = {arXiv:1609.09011v3}
}

@article{Tropp,
  author = {Tropp, Joel A.},
  title = {User-friendly tail bounds for sums of random matrices},
  journal = {Foundations of Computational Mathematics},
  volume = {12},
  number = {4},
  pages = {389--434},
  year = {2012},
  doi = {10.1007/s10208-011-9099-z},
  url = {https://arxiv.org/abs/1004.4389v7},
  note = {arXiv:1004.4389v7}
}

@article{ValkoVirag,
  author = {Valk{\'o}, Benedek and Vir{\'a}g, B{\'a}lint},
  title = {Continuum limits of random matrices and the {Brownian} carousel},
  journal = {Inventiones Mathematicae},
  volume = {177},
  number = {3},
  pages = {463--508},
  year = {2009},
  doi = {10.1007/s00222-009-0180-z},
  url = {https://arxiv.org/abs/0712.2000v4},
  note = {arXiv:0712.2000v4}
}

@article{BackhauszSzegedy,
  author = {Backhausz, {\'A}gnes and Szegedy, Bal{\'a}zs},
  title = {On the almost eigenvectors of random regular graphs},
  journal = {The Annals of Probability},
  volume = {47},
  number = {3},
  pages = {1677--1725},
  year = {2019},
  doi = {10.1214/18-AOP1294},
  url = {https://backhauszagi.web.elte.hu/aop1294.pdf},
  note = {Theorem and lemma numbering follows the published version}
}

@article{Kesten,
  author = {Kesten, Harry},
  title = {Symmetric random walks on groups},
  journal = {Transactions of the American Mathematical Society},
  volume = {92},
  number = {2},
  pages = {336--354},
  year = {1959},
  doi = {10.1090/S0002-9947-1959-0109367-6}
}

@article{McKay,
  author = {McKay, Brendan D.},
  title = {The expected eigenvalue distribution of a large regular graph},
  journal = {Linear Algebra and its Applications},
  volume = {40},
  pages = {203--216},
  year = {1981},
  doi = {10.1016/0024-3795(81)90150-6},
  url = {https://users.cecs.anu.edu.au/~bdm/papers/RandRegEigenvalues.pdf}
}

@incollection{JakobsonEtAl,
  author = {Jakobson, Dmitry and Miller, Stephen D. and Rivin, Igor and Rudnick, Zeev},
  title = {Eigenvalue spacings for regular graphs},
  booktitle = {Emerging Applications of Number Theory},
  editor = {Hejhal, Dennis A. and Friedman, Joel and Gutzwiller, Martin C. and Odlyzko, Andrew M.},
  series = {The IMA Volumes in Mathematics and its Applications},
  volume = {109},
  pages = {317--327},
  publisher = {Springer},
  address = {New York},
  year = {1999},
  doi = {10.1007/978-1-4612-1544-8_12},
  url = {https://arxiv.org/abs/hep-th/0310002v1}
}

@article{BauerschmidtEtAl,
  author = {Bauerschmidt, Roland and Huang, Jiaoyang and Knowles, Antti and Yau, Horng-Tzer},
  title = {Bulk eigenvalue statistics for random regular graphs},
  journal = {The Annals of Probability},
  volume = {45},
  number = {6A},
  pages = {3626--3663},
  year = {2017},
  doi = {10.1214/16-AOP1145},
  url = {https://arxiv.org/abs/1505.06700v3}
}

@misc{BourgadeHuang,
  author = {Bourgade, Paul and Huang, Jiaoyang},
  title = {Loop equations characterize random matrix statistics},
  year = {2026},
  howpublished = {arXiv:2607.07617v2},
  url = {https://arxiv.org/abs/2607.07617v2},
  note = {Revised 9 September 2026}
}

@article{BauerschmidtKnowlesYauLocal,
  author = {Bauerschmidt, Roland and Knowles, Antti and Yau, Horng-Tzer},
  title = {Local semicircle law for random regular graphs},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {70},
  number = {10},
  pages = {1898--1960},
  year = {2017},
  doi = {10.1002/cpa.21709},
  url = {https://arxiv.org/abs/1503.08702v5}
}

@article{BauerschmidtHuangYauLocal,
  author = {Bauerschmidt, Roland and Huang, Jiaoyang and Yau, Horng-Tzer},
  title = {Local {Kesten--McKay} law for random regular graphs},
  journal = {Communications in Mathematical Physics},
  volume = {369},
  number = {2},
  pages = {523--636},
  year = {2019},
  doi = {10.1007/s00220-019-03345-3},
  url = {https://arxiv.org/abs/1609.09052v3}
}

@incollection{ForresterRains,
  author = {Forrester, Peter J. and Rains, Eric M.},
  title = {Interrelationships between orthogonal, unitary and symplectic matrix ensembles},
  booktitle = {Random Matrix Models and Their Applications},
  editor = {Bleher, Pavel and Its, Alexander},
  series = {Mathematical Sciences Research Institute Publications},
  volume = {40},
  pages = {171--207},
  publisher = {Cambridge University Press},
  year = {2001},
  url = {https://arxiv.org/abs/solv-int/9907008v2}
}

@article{BollobasPairing,
  author = {Bollob{\'a}s, B{\'e}la},
  title = {A probabilistic proof of an asymptotic formula for the number of labelled regular graphs},
  journal = {European Journal of Combinatorics},
  volume = {1},
  number = {4},
  pages = {311--316},
  year = {1980},
  doi = {10.1016/S0195-6698(80)80030-8}
}

@article{BackhauszSzegedyTrees,
  author = {Backhausz, {\'A}gnes and Szegedy, Bal{\'a}zs},
  title = {On large girth regular graphs and random processes on trees},
  journal = {Random Structures \& Algorithms},
  volume = {53},
  number = {3},
  pages = {389--416},
  year = {2018},
  url = {https://arxiv.org/abs/1406.4420v2}
}

@article{BackhauszBordenaveSzegedy,
  author = {Backhausz, {\'A}gnes and Bordenave, Charles and Szegedy, Bal{\'a}zs},
  title = {Typicality and entropy of processes on infinite trees},
  journal = {Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques},
  volume = {58},
  number = {4},
  pages = {1959--1980},
  year = {2022},
  url = {https://arxiv.org/abs/2102.02653v2}
}

@misc{HeHuangYauWaves,
  author = {He, Yukun and Huang, Jiaoyang and Yau, Horng-Tzer},
  title = {Gaussian waves and edge eigenvectors of random regular graphs},
  year = {2025},
  howpublished = {arXiv:2502.08897v1},
  url = {https://arxiv.org/abs/2502.08897v1}
}

@misc{DemboMcKenzie,
  author = {Dembo, Amir and McKenzie, Theo},
  title = {The {Gaussian} wave for graphs of finite cone type},
  year = {2026},
  howpublished = {arXiv:2603.04386v1},
  url = {https://arxiv.org/abs/2603.04386v1}
}

@article{CsokaEtAl,
  author = {Cs{\'o}ka, Endre and Gerencs{\'e}r, Bal{\'a}zs and Harangi, Viktor and Vir{\'a}g, B{\'a}lint},
  title = {Invariant {Gaussian} processes and independent sets on regular graphs of large girth},
  journal = {Random Structures \& Algorithms},
  volume = {47},
  pages = {284--303},
  year = {2015},
  doi = {10.1002/rsa.20547},
  url = {https://arxiv.org/abs/1305.3977}
}

@article{ElonEigenvectors,
  author = {Elon, Yehonatan},
  title = {Eigenvectors of the discrete {Laplacian} on regular graphs---a statistical approach},
  journal = {Journal of Physics A: Mathematical and Theoretical},
  volume = {41},
  pages = {435203},
  year = {2008},
  doi = {10.1088/1751-8113/41/43/435203},
  url = {https://arxiv.org/abs/0804.2771}
}

@article{LandonYau,
  author = {Landon, Benjamin and Yau, Horng-Tzer},
  title = {Convergence of local statistics of {Dyson Brownian} motion},
  journal = {Communications in Mathematical Physics},
  volume = {355},
  pages = {949--1000},
  year = {2017},
  doi = {10.1007/s00220-017-2955-1},
  url = {https://arxiv.org/abs/1504.03605v2}
}

@article{DysonBrownian,
  author = {Dyson, Freeman J.},
  title = {A {Brownian}-motion model for the eigenvalues of a random matrix},
  journal = {Journal of Mathematical Physics},
  volume = {3},
  number = {6},
  pages = {1191--1198},
  year = {1962},
  doi = {10.1063/1.1703862}
}

@article{ChatterjeeLindeberg,
  author = {Chatterjee, Sourav},
  title = {A generalization of the {Lindeberg} principle},
  journal = {The Annals of Probability},
  volume = {34},
  number = {6},
  pages = {2061--2076},
  year = {2006},
  doi = {10.1214/009117906000000575},
  url = {https://arxiv.org/abs/math/0508519v3}
}

@article{Biane,
  author = {Biane, Philippe},
  title = {On the free convolution with a semi-circular distribution},
  journal = {Indiana University Mathematics Journal},
  volume = {46},
  number = {3},
  pages = {705--718},
  year = {1997},
  doi = {10.1512/iumj.1997.46.1467}
}

@misc{HuangMcKenzieYau,
  author = {Huang, Jiaoyang and McKenzie, Theo and Yau, Horng-Tzer},
  title = {{Ramanujan} property and edge universality of random regular graphs},
  year = {2025},
  howpublished = {arXiv:2412.20263v2},
  url = {https://arxiv.org/abs/2412.20263v2},
  note = {First posted 28 December 2024; revised 2 February 2025}
}