@article{lundgren1983,
  author = {Lundgren, Lars and Svedlindh, Per and Nordblad, Per and Beckman, Olov},
  title = {Dynamics of the Relaxation-Time Spectrum in a {CuMn} Spin-Glass},
  journal = {Physical Review Letters},
  volume = {51}, pages = {911--914}, year = {1983},
  doi = {10.1103/PhysRevLett.51.911}
}

@incollection{vincent1997,
  author = {Vincent, Eric and Hammann, Jacques and Ocio, Miguel and Bouchaud, Jean-Philippe and Cugliandolo, Leticia F.},
  title = {Slow dynamics and aging in spin glasses},
  booktitle = {Complex Behaviour of Glassy Systems},
  editor = {Rub{\'i}, Miguel and P{\'e}rez-Vicente, Conrado},
  series = {Lecture Notes in Physics}, volume = {492},
  publisher = {Springer}, address = {Berlin, Heidelberg},
  pages = {184--219}, year = {1997},
  doi = {10.1007/BFb0104827},
  eprint = {cond-mat/9607224}, archivePrefix = {arXiv}
}

@article{bouchaud1992,
  author = {Bouchaud, Jean-Philippe},
  title = {Weak ergodicity breaking and aging in disordered systems},
  journal = {Journal de Physique I},
  volume = {2}, number = {9}, pages = {1705--1713}, year = {1992},
  doi = {10.1051/jp1:1992238}
}

@article{derrida1980,
  author = {Derrida, Bernard},
  title = {Random-Energy Model: Limit of a Family of Disordered Models},
  journal = {Physical Review Letters},
  volume = {45}, pages = {79--82}, year = {1980},
  doi = {10.1103/PhysRevLett.45.79}
}

@article{grossmezard1984,
  author = {Gross, David J. and M{\'e}zard, Marc},
  title = {The simplest spin glass},
  journal = {Nuclear Physics B},
  volume = {240}, number = {4}, pages = {431--452}, year = {1984},
  doi = {10.1016/0550-3213(84)90237-2}
}

@article{gardner1985,
  author = {Gardner, Elizabeth},
  title = {Spin glasses with $p$-spin interactions},
  journal = {Nuclear Physics B},
  volume = {257}, pages = {747--765}, year = {1985},
  doi = {10.1016/0550-3213(85)90374-8}
}

@article{sz1981,
  author = {Sompolinsky, Haim and Zippelius, Annette},
  title = {Dynamic Theory of the Spin-Glass Phase},
  journal = {Physical Review Letters},
  volume = {47}, pages = {359--362}, year = {1981},
  doi = {10.1103/PhysRevLett.47.359}
}

@article{sz1982,
  author = {Sompolinsky, Haim and Zippelius, Annette},
  title = {Relaxational dynamics of the {Edwards--Anderson} model and the mean-field theory of spin-glasses},
  journal = {Physical Review B},
  volume = {25}, pages = {6860--6875}, year = {1982},
  doi = {10.1103/PhysRevB.25.6860}
}

@article{kt1987a,
  author = {Kirkpatrick, T. R. and Thirumalai, Devarajan},
  title = {Dynamics of the Structural Glass Transition and the $p$-Spin-Interaction Spin-Glass Model},
  journal = {Physical Review Letters},
  volume = {58}, pages = {2091--2094}, year = {1987},
  doi = {10.1103/PhysRevLett.58.2091}
}

@article{kt1987b,
  author = {Kirkpatrick, T. R. and Thirumalai, Devarajan},
  title = {$p$-spin-interaction spin-glass models: Connections with the structural glass problem},
  journal = {Physical Review B},
  volume = {36}, pages = {5388--5397}, year = {1987},
  doi = {10.1103/PhysRevB.36.5388}
}

@article{ktw1989,
  author = {Kirkpatrick, T. R. and Thirumalai, Devarajan and Wolynes, Peter G.},
  title = {Scaling concepts for the dynamics of viscous liquids near an ideal glassy state},
  journal = {Physical Review A},
  volume = {40}, pages = {1045--1054}, year = {1989},
  doi = {10.1103/PhysRevA.40.1045}
}


@article{bgs1984,
  author = {Bengtzelius, U. and G{\"o}tze, W. and Sj{\"o}lander, A.},
  title = {Dynamics of supercooled liquids and the glass transition},
  journal = {Journal of Physics C: Solid State Physics},
  volume = {17},
  pages = {5915--5934},
  year = {1984},
  doi = {10.1088/0022-3719/17/33/005}
}

@article{leutheusser1984,
  author = {Leutheusser, E.},
  title = {Dynamical model of the liquid-glass transition},
  journal = {Physical Review A},
  volume = {29},
  number = {5},
  pages = {2765--2773},
  year = {1984},
  doi = {10.1103/PhysRevA.29.2765}
}

@article{goetze1984,
  author = {G{\"o}tze, Wolfgang},
  title = {Some aspects of phase transitions described by the
           self consistent current relaxation theory},
  journal = {Zeitschrift f{\"u}r Physik B Condensed Matter},
  volume = {56},
  pages = {139--154},
  year = {1984},
  doi = {10.1007/BF01469695}
}

@article{goetze1998,
  author = {G{\"o}tze, Wolfgang},
  title = {The essentials of the mode-coupling theory for glassy dynamics},
  journal = {Condensed Matter Physics},
  volume = {1},
  number = {4},
  pages = {873--904},
  year = {1998},
  doi = {10.5488/CMP.1.4.873},
  url = {https://icmp.lviv.ua/journal/zbirnyk.16/008/art08.pdf}
}


@article{kpv1993,
  author = {Kurchan, Jorge and Parisi, Giorgio and Virasoro, Miguel Angel},
  title = {Barriers and metastable states as saddle points in the replica approach},
  journal = {Journal de Physique I},
  volume = {3}, number = {8}, pages = {1819--1838}, year = {1993},
  doi = {10.1051/jp1:1993217}
}

@article{cgp1998,
  author = {Cavagna, Andrea and Giardina, Irene and Parisi, Giorgio},
  title = {Stationary points of the {Thouless--Anderson--Palmer} free energy},
  journal = {Physical Review B},
  volume = {57}, pages = {11251--11257}, year = {1998},
  doi = {10.1103/PhysRevB.57.11251},
  eprint = {cond-mat/9710272}, archivePrefix = {arXiv}
}

@article{kurchanlaloux1996,
  author = {Kurchan, Jorge and Laloux, Laurent},
  title = {Phase space geometry and slow dynamics},
  journal = {Journal of Physics A: Mathematical and General},
  volume = {29}, number = {9}, pages = {1929--1948}, year = {1996},
  doi = {10.1088/0305-4470/29/9/009},
  eprint = {cond-mat/9510079}, archivePrefix = {arXiv}
}

@article{ckp1997,
  author = {Cugliandolo, Leticia F. and Kurchan, Jorge and Peliti, Luca},
  title = {Energy flow, partial equilibration, and effective temperatures in systems with slow dynamics},
  journal = {Physical Review E},
  volume = {55}, number = {4}, pages = {3898--3914}, year = {1997},
  doi = {10.1103/PhysRevE.55.3898},
  eprint = {cond-mat/9611044}, archivePrefix = {arXiv}
}

@article{fmpp1998,
  author = {Franz, Silvio and M{\'e}zard, Marc and Parisi, Giorgio and Peliti, Luca},
  title = {Measuring Equilibrium Properties in Aging Systems},
  journal = {Physical Review Letters},
  volume = {81}, pages = {1758--1761}, year = {1998},
  doi = {10.1103/PhysRevLett.81.1758},
  eprint = {cond-mat/9803108}, archivePrefix = {arXiv}
}

@article{altieri2020,
  author = {Altieri, Ada and Biroli, Giulio and Cammarota, Chiara},
  title = {Dynamical Mean-Field Theory and Aging Dynamics},
  journal = {Journal of Physics A: Mathematical and Theoretical},
  volume = {53}, pages = {375006}, year = {2020},
  doi = {10.1088/1751-8121/aba3dd},
  eprint = {2005.05118}, archivePrefix = {arXiv}
}

@article{chamon2002,
  author = {Chamon, Claudio and Kennett, Malcolm P. and Castillo, Horacio E. and Cugliandolo, Leticia F.},
  title = {Separation of time scales and reparametrization invariance for aging systems},
  journal = {Physical Review Letters},
  volume = {89}, pages = {217201}, year = {2002},
  doi = {10.1103/PhysRevLett.89.217201},
  eprint = {cond-mat/0109150}, archivePrefix = {arXiv}
}

@article{folena2020,
  author = {Folena, Giampaolo and Franz, Silvio and Ricci-Tersenghi, Federico},
  title = {Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed $p$-Spin Model},
  journal = {Physical Review X},
  volume = {10}, pages = {031045}, year = {2020},
  doi = {10.1103/PhysRevX.10.031045},
  eprint = {1903.01421}, archivePrefix = {arXiv}
}

@article{folenazamponi2023,
  author = {Folena, Giampaolo and Zamponi, Francesco},
  title = {On weak ergodicity breaking in mean-field spin glasses},
  journal = {SciPost Physics},
  volume = {15}, number = {3}, pages = {109}, year = {2023},
  doi = {10.21468/SciPostPhys.15.3.109},
  eprint = {2303.00026}, archivePrefix = {arXiv}
}

@article{lang2025,
  author = {Lang, Johannes and Sachdev, Subir and Diehl, Sebastian},
  title = {Numerical Renormalization of Glassy Dynamics},
  journal = {Physical Review Letters},
  volume = {135}, pages = {247101}, year = {2025},
  doi = {10.1103/z64g-nqs6},
  eprint = {2504.06849}, archivePrefix = {arXiv}
}


@article{bg1995,
  author = {Ben Arous, G{\'e}rard and Guionnet, Alice},
  title = {Large deviations for {Langevin} spin glass dynamics},
  journal = {Probability Theory and Related Fields},
  volume = {102}, number = {4}, pages = {455--509}, year = {1995},
  doi = {10.1007/BF01198846}
}

@article{bg1997,
  author = {Ben Arous, G{\'e}rard and Guionnet, Alice},
  title = {Symmetric {Langevin} spin glass dynamics},
  journal = {The Annals of Probability},
  volume = {25}, number = {3}, pages = {1367--1422}, year = {1997},
  doi = {10.1214/aop/1024404517}
}

@article{grunwald1996,
  author = {Grunwald, Malte},
  title = {Sanov results for {Glauber} spin-glass dynamics},
  journal = {Probability Theory and Related Fields},
  volume = {106}, number = {2}, pages = {187--232}, year = {1996},
  doi = {10.1007/s004400050062}
}

@article{guionnet1997,
  author = {Guionnet, Alice},
  title = {Averaged and quenched propagation of chaos for spin glass dynamics},
  journal = {Probability Theory and Related Fields},
  volume = {109}, number = {2}, pages = {183--215}, year = {1997},
  doi = {10.1007/s004400050130}
}

@incollection{ba2002,
  author = {Ben Arous, G{\'e}rard},
  title = {Aging and Spin-glass Dynamics},
  booktitle = {Proceedings of the International Congress of Mathematicians, Beijing 2002},
  volume = {III}, pages = {3--14},
  publisher = {Higher Education Press}, address = {Beijing}, year = {2002},
  eprint = {math/0304364}, archivePrefix = {arXiv}
}

@incollection{guionnet2007,
  author = {Guionnet, Alice},
  title = {Dynamics for Spherical Models of Spin-Glass and Aging},
  editor = {Bolthausen, Erwin and Bovier, Anton},
  booktitle = {Spin Glasses},
  series = {Lecture Notes in Mathematics}, volume = {1900},
  pages = {117--144}, publisher = {Springer}, year = {2007},
  doi = {10.1007/978-3-540-40908-3_5}
}

@article{dlz2021,
  author = {Dembo, Amir and Lubetzky, Eyal and Zeitouni, Ofer},
  title = {Universality for {Langevin}-like spin glass dynamics},
  journal = {The Annals of Applied Probability},
  volume = {31}, number = {6}, pages = {2864--2880}, year = {2021},
  doi = {10.1214/21-AAP1665},
  eprint = {1911.08001}, archivePrefix = {arXiv}
}

@misc{ccm2021,
  author = {Celentano, Michael and Cheng, Chen and Montanari, Andrea},
  title = {The high-dimensional asymptotics of first order methods with random data},
  year = {2021},
  eprint = {2112.07572}, archivePrefix = {arXiv},
  note = {arXiv:2112.07572, version 3, April 2026}
}

@article{gerbelot2024,
  author = {Gerbelot, C{\'e}dric and Troiani, Emanuele and Mignacco, Francesca and Krzakala, Florent and Zdeborov{\'a}, Lenka},
  title = {Rigorous Dynamical Mean-Field Theory for Stochastic Gradient Descent Methods},
  journal = {SIAM Journal on Mathematics of Data Science},
  volume = {6}, number = {2}, pages = {400--427}, year = {2024},
  doi = {10.1137/23M1594388},
  eprint = {2210.06591}, archivePrefix = {arXiv}
}

@inproceedings{dandi2026,
  author = {Dandi, Yatin and Gamarnik, David and Pernice, Francisco and Zdeborov{\'a}, Lenka},
  title = {Rigorous Asymptotics for First-Order Algorithms Through the Dynamical Cavity Method},
  booktitle = {Proceedings of the Thirty Ninth Conference on Learning Theory},
  editor = {Hanneke, Steve and Lattimore, Tor},
  series = {Proceedings of Machine Learning Research},
  volume = {336}, pages = {1611--1646}, publisher = {PMLR}, year = {2026},
  eprint = {2603.14573}, archivePrefix = {arXiv}
}

@article{lss2023,
  author = {Liang, Tengyuan and Sen, Subhabrata and Sur, Pragya},
  title = {High-dimensional asymptotics of {Langevin} dynamics in spiked matrix models},
  journal = {Information and Inference},
  volume = {12}, number = {4}, pages = {2720--2752}, year = {2023},
  doi = {10.1093/imaiai/iaad042},
  eprint = {2204.04476}, archivePrefix = {arXiv}
}

@misc{fan2025a,
  author = {Fan, Zhou and Ko, Justin and Loureiro, Bruno and Lu, Yue M. and Shen, Yandi},
  title = {Dynamical mean-field analysis of adaptive {Langevin} diffusions: Propagation-of-chaos and convergence of the linear response},
  year = {2025},
  eprint = {2504.15556}, archivePrefix = {arXiv},
  note = {arXiv:2504.15556, version 2, November 2025}
}

@misc{fan2025b,
  author = {Fan, Zhou and Ko, Justin and Loureiro, Bruno and Lu, Yue M. and Shen, Yandi},
  title = {Dynamical mean-field analysis of adaptive {Langevin} diffusions: Replica-symmetric fixed point and empirical {Bayes}},
  year = {2025},
  eprint = {2504.15558}, archivePrefix = {arXiv},
  note = {arXiv:2504.15558, version 2, November 2025}
}

@misc{fan2026,
  author = {Fan, Zhou and Misiakiewicz, Theodor and Wang, Leda and Wen, Garrett G.},
  title = {Dynamical mean-field limit and replica-symmetric free energy for the orthogonally-invariant {SK} model},
  year = {2026},
  eprint = {2607.10102}, archivePrefix = {arXiv},
  note = {arXiv:2607.10102, version 2, September 2026}
}


@article{bbg2003a,
  author = {Ben Arous, G{\'e}rard and Bovier, Anton and Gayrard, V{\'e}ronique},
  title = {{Glauber} Dynamics of the Random Energy Model. {I}. Metastable Motion on the Extreme States},
  journal = {Communications in Mathematical Physics},
  volume = {235}, number = {3}, pages = {379--425}, year = {2003},
  doi = {10.1007/s00220-003-0798-4}
}

@article{bbg2003b,
  author = {Ben Arous, G{\'e}rard and Bovier, Anton and Gayrard, V{\'e}ronique},
  title = {{Glauber} Dynamics of the Random Energy Model. {II}. Aging Below the Critical Temperature},
  journal = {Communications in Mathematical Physics},
  volume = {236}, number = {1}, pages = {1--54}, year = {2003},
  doi = {10.1007/s00220-003-0799-3}
}

@incollection{bc2006,
  author = {Ben Arous, G{\'e}rard and {\v{C}}ern{\'y}, Ji{\v{r}}{\'i}},
  title = {Dynamics of Trap Models},
  booktitle = {Mathematical Statistical Physics},
  series = {Les Houches}, volume = {83}, pages = {331--394},
  publisher = {Elsevier}, year = {2006},
  doi = {10.1016/S0924-8099(06)80045-4},
  eprint = {math/0603344}, archivePrefix = {arXiv}
}

@article{bc2008,
  author = {Ben Arous, G{\'e}rard and {\v{C}}ern{\'y}, Ji{\v{r}}{\'i}},
  title = {The arcsine law as a universal aging scheme for trap models},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {61}, number = {3}, pages = {289--329}, year = {2008},
  doi = {10.1002/cpa.20177},
  eprint = {math/0603340}, archivePrefix = {arXiv}
}

@article{bbc2008,
  author = {Ben Arous, G{\'e}rard and Bovier, Anton and {\v{C}}ern{\'y}, Ji{\v{r}}{\'i}},
  title = {Universality of the {REM} for Dynamics of Mean-Field Spin Glasses},
  journal = {Communications in Mathematical Physics},
  volume = {282}, number = {3}, pages = {663--695}, year = {2008},
  doi = {10.1007/s00220-008-0565-7},
  eprint = {0706.2135}, archivePrefix = {arXiv}
}

@article{bg2012,
  author = {Ben Arous, G{\'e}rard and G{\"u}n, Onur},
  title = {Universality and extremal aging for dynamics of spin glasses on subexponential time scales},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {65}, number = {1}, pages = {77--127}, year = {2012},
  doi = {10.1002/cpa.20372},
  eprint = {1010.5190}, archivePrefix = {arXiv}
}

@article{boviergayrard2013,
  author = {Bovier, Anton and Gayrard, V{\'e}ronique},
  title = {Convergence of clock processes in random environments and ageing in the $p$-spin {SK} model},
  journal = {The Annals of Probability},
  volume = {41}, number = {2}, pages = {817--847}, year = {2013},
  doi = {10.1214/11-AOP705},
  eprint = {1008.3839}, archivePrefix = {arXiv}
}

@article{cw2017,
  author = {{\v{C}}ern{\'y}, Ji{\v{r}}{\'i} and Wassmer, Tobias},
  title = {Aging of the {Metropolis} dynamics on the random energy model},
  journal = {Probability Theory and Related Fields},
  volume = {167}, number = {1--2}, pages = {253--303}, year = {2017},
  doi = {10.1007/s00440-015-0681-1},
  eprint = {1502.04535}, archivePrefix = {arXiv}
}

@article{gayrard2019,
  author = {Gayrard, V{\'e}ronique},
  title = {Aging in {Metropolis} dynamics of the {REM}: a proof},
  journal = {Probability Theory and Related Fields},
  volume = {174}, number = {1--2}, pages = {501--551}, year = {2019},
  doi = {10.1007/s00440-018-0873-6},
  eprint = {1602.06081}, archivePrefix = {arXiv}
}


@article{ab2013,
  author = {Auffinger, Antonio and Ben Arous, G{\'e}rard},
  title = {Complexity of random smooth functions on the high-dimensional sphere},
  journal = {The Annals of Probability},
  volume = {41}, number = {6}, pages = {4214--4247}, year = {2013},
  doi = {10.1214/13-AOP862},
  eprint = {1110.5872}, archivePrefix = {arXiv}
}

@article{subag2017,
  author = {Subag, Eliran},
  title = {The complexity of spherical $p$-spin models---a second moment approach},
  journal = {The Annals of Probability},
  volume = {45}, number = {5}, pages = {3385--3450}, year = {2017},
  doi = {10.1214/16-AOP1139},
  eprint = {1504.02251}, archivePrefix = {arXiv}
}

@inproceedings{montanari2019,
  author = {Montanari, Andrea},
  title = {Optimization of the {Sherrington--Kirkpatrick} Hamiltonian},
  booktitle = {2019 IEEE 60th Annual Symposium on Foundations of Computer Science},
  pages = {1417--1433}, publisher = {IEEE}, year = {2019},
  doi = {10.1109/FOCS.2019.00087},
  eprint = {1812.10897}, archivePrefix = {arXiv}
}

@article{eams2021,
  author = {El Alaoui, Ahmed and Montanari, Andrea and Sellke, Mark},
  title = {Optimization of mean-field spin glasses},
  journal = {The Annals of Probability},
  volume = {49}, number = {6}, pages = {2922--2960}, year = {2021},
  doi = {10.1214/21-AOP1519},
  eprint = {2001.00904}, archivePrefix = {arXiv}
}

@article{hs2024amp,
  author = {Huang, Brice and Sellke, Mark},
  title = {Optimization Algorithms for Multi-species Spherical Spin Glasses},
  journal = {Journal of Statistical Physics},
  volume = {191},
  pages = {29},
  year = {2024},
  doi = {10.1007/s10955-024-03242-7},
  eprint = {2308.09672},
  archivePrefix = {arXiv}
}

@article{gj2019,
  author = {Gheissari, Reza and Jagannath, Aukosh},
  title = {On the Spectral Gap of Spherical Spin Glass Dynamics},
  journal = {Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques},
  volume = {55}, number = {2}, pages = {756--776}, year = {2019},
  doi = {10.1214/18-AIHP897},
  eprint = {1608.06609}, archivePrefix = {arXiv}
}

@article{bgj2020,
  author = {Ben Arous, G{\'e}rard and Gheissari, Reza and Jagannath, Aukosh},
  title = {Bounding Flows for Spherical Spin Glass Dynamics},
  journal = {Communications in Mathematical Physics},
  volume = {373}, number = {3}, pages = {1011--1048}, year = {2020},
  doi = {10.1007/s00220-019-03649-4},
  eprint = {1808.00929}, archivePrefix = {arXiv}
}

@article{bj2024,
  author = {Ben Arous, G{\'e}rard and Jagannath, Aukosh},
  title = {Shattering versus metastability in spin glasses},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {77}, number = {1}, pages = {139--176}, year = {2024},
  doi = {10.1002/cpa.22133},
  eprint = {2104.08299}, archivePrefix = {arXiv}
}


@misc{lang2026,
  author = {Lang, Johannes and Citro, Vincenzo and Leuzzi, Luca and Ricci-Tersenghi, Federico},
  title = {Aging Phase Diagram and Exact Asymptotic Energies of Mixed Spherical Spin Glasses},
  year = {2026},
  eprint = {2608.20623}, archivePrefix = {arXiv},
  note = {arXiv:2608.20623, version 1, August 2026}
}

@misc{cipolloni2026,
  author = {Cipolloni, Riccardo and Cugliandolo, Leticia F.},
  title = {Coupling spherical $p$-spin systems},
  year = {2026},
  eprint = {2609.17522}, archivePrefix = {arXiv},
  note = {arXiv:2609.17522, version 1, September 2026}
}

@article{citro2025,
  author = {Citro, Vincenzo and Ricci-Tersenghi, Federico},
  title = {Strong Ergodicity Breaking in Dynamical Mean-Field Equations for Mixed $p$-Spin Glasses},
  journal = {Physical Review Letters},
  volume = {135}, number = {24}, pages = {247102}, year = {2025},
  doi = {10.1103/lvmp-pydk},
  eprint = {2504.12367}, archivePrefix = {arXiv}
}

@article{ghimenti2026,
  author = {Ghimenti, Federico and Berthier, Ludovic and Kurchan, Jorge and van Wijland, Fr{\'e}d{\'e}ric},
  title = {Clever algorithms for glasses work by time reparameterization},
  journal = {Proceedings of the National Academy of Sciences},
  volume = {123},
  number = {4},
  pages = {e2520818123},
  year = {2026},
  doi = {10.1073/pnas.2520818123},
  url = {https://doi.org/10.1073/pnas.2520818123},
  note = {Correction: {\em Proc. Natl. Acad. Sci. USA} 123(12), e2606723123 (2026), doi:10.1073/pnas.2606723123}
}