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@article{Biroli_1999_Dynamical,
author = {Biroli, Giulio},
title = {Dynamical {TAP} approach to mean field glassy systems},
journal = {Journal of Physics A: Mathematical and General},
publisher = {IOP Publishing},
year = {1999},
month = {11},
number = {48},
volume = {32},
pages = {8365--8388},
url = {https://doi.org/10.1088%2F0305-4470%2F32%2F48%2F301},
doi = {10.1088/0305-4470/32/48/301}
}
@article{Bray_2007_Statistics,
author = {Bray, Alan J. and Dean, David S.},
title = {Statistics of Critical Points of {Gaussian} Fields on Large-Dimensional Spaces},
journal = {Physical Review Letters},
publisher = {American Physical Society (APS)},
year = {2007},
month = {4},
number = {15},
volume = {98},
pages = {150201},
url = {https://doi.org/10.1103%2Fphysrevlett.98.150201},
doi = {10.1103/physrevlett.98.150201}
}
@article{Folena_2020_Rethinking,
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},
publisher = {American Physical Society},
year = {2020},
month = {8},
volume = {10},
pages = {031045},
url = {https://link.aps.org/doi/10.1103/PhysRevX.10.031045},
doi = {10.1103/PhysRevX.10.031045},
issue = {3},
numpages = {26}
}
@article{Folena_2021_Gradient,
author = {Folena, Giampaolo and Franz, Silvio and Ricci-Tersenghi, Federico},
title = {Gradient descent dynamics in the mixed {$p$}-spin spherical model: finite-size simulations and comparison with mean-field integration},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
publisher = {IOP Publishing},
year = {2021},
month = {3},
number = {3},
volume = {2021},
pages = {033302},
url = {https://doi.org/10.1088%2F1742-5468%2Fabe29f},
doi = {10.1088/1742-5468/abe29f}
}
@article{Franz_1995_Recipes,
author = {Franz, Silvio and Parisi, Giorgio},
title = {Recipes for Metastable States in Spin Glasses},
journal = {Journal de Physique I},
publisher = {EDP Sciences},
year = {1995},
month = {11},
number = {11},
volume = {5},
pages = {1401--1415},
url = {https://doi.org/10.1051%2Fjp1%3A1995201},
doi = {10.1051/jp1:1995201}
}
@article{Ikeda_2023_Bose-Einstein-like,
author = {Ikeda, Harukuni},
title = {{Bose}--{Einstein}-like condensation of deformed random matrix: a replica approach},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
publisher = {IOP Publishing},
year = {2023},
month = {2},
number = {2},
volume = {2023},
pages = {023302},
url = {https://doi.org/10.1088%2F1742-5468%2Facb7d6},
doi = {10.1088/1742-5468/acb7d6}
}
@article{Kac_1943_On,
author = {Kac, M.},
title = {On the average number of real roots of a random algebraic equation},
journal = {Bulletin of the American Mathematical Society},
publisher = {American Mathematical Society},
year = {1943},
month = {4},
number = {4},
volume = {49},
pages = {314--320},
url = {https://projecteuclid.org:443/euclid.bams/1183505112}
}
@article{Rice_1944_Mathematical,
author = {Rice, S. O.},
title = {Mathematical Analysis of Random Noise},
journal = {Bell System Technical Journal},
publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
year = {1944},
month = {7},
number = {3},
volume = {23},
pages = {282--332},
url = {https://doi.org/10.1002%2Fj.1538-7305.1944.tb00874.x},
doi = {10.1002/j.1538-7305.1944.tb00874.x}
}
@article{Ros_2019_Complex,
author = {Ros, Valentina and Ben Arous, Gérard and Biroli, Giulio and Cammarota, Chiara},
title = {Complex Energy Landscapes in Spiked-Tensor and Simple Glassy Models: Ruggedness, Arrangements of Local Minima, and Phase Transitions},
journal = {Physical Review X},
publisher = {American Physical Society (APS)},
year = {2019},
month = {1},
number = {1},
volume = {9},
pages = {011003},
url = {https://doi.org/10.1103%2Fphysrevx.9.011003},
doi = {10.1103/physrevx.9.011003}
}
@article{Ros_2019_Complexity,
author = {Ros, V. and Biroli, G. and Cammarota, C.},
title = {Complexity of energy barriers in mean-field glassy systems},
journal = {EPL (Europhysics Letters)},
publisher = {IOP Publishing},
year = {2019},
month = {5},
number = {2},
volume = {126},
pages = {20003},
url = {https://doi.org/10.1209%2F0295-5075%2F126%2F20003},
doi = {10.1209/0295-5075/126/20003}
}
@article{Ros_2020_Distribution,
author = {Ros, Valentina},
title = {Distribution of rare saddles in the {$p$}-spin energy landscape},
journal = {Journal of Physics A: Mathematical and Theoretical},
publisher = {IOP Publishing},
year = {2020},
month = {3},
number = {12},
volume = {53},
pages = {125002},
url = {https://doi.org/10.1088%2F1751-8121%2Fab73ac},
doi = {10.1088/1751-8121/ab73ac}
}
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