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We consider the algorithmic problem of finding a near ground state (near optimal solution) of a $p$-spin model.
1911
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Mohsen Bayati and Andrea Montanari, The dynamics of message passing on dense graphs, with applications to compressed sensing , IEEE Transactions on Information Theory 57
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A. Coja-Oghlan and C. Efthymiou, On independent sets in random graphs , Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2011, pp. 136–144
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Gerald Teschl, Ordinary differential equations and dynamical systems , vol. 140, American Mathematical Soc., 2012
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Adel Javanmard and Andrea Montanari, State evolution for general approximate message passing algorithms, with applications to spatial coupling , Information and Inference: A Journal of the IMA 2
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Dmitry Panchenko, The sherrington-kirkpatrick model , Springer Science & Business Media, 2013
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Erwin Bolthausen, An iterative construction of solutions of the tap equations for the sherrington–kirkpatrick model , Communications in Mathematical Physics 325
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Antonio Auffinger and Wei-Kuo Chen, On properties of Parisi measures , Probab. Theory Related Fields 161
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David Gamarnik and Madhu Sudan, Limits of local algorithms over sparse random graphs , Annals of Probability 45
2017
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Mustazee Rahman, Balint Virag, et al., Local algorithms for independent sets are half-optimal , The Annals of Probability 45
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Gérard Ben Arous and Aukosh Jagannath, Spectral gap estimates in mean field spin glasses , Comm. Math. Phys. 361
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Amin Coja-Oghlan, Amir Haqshenas, and Samuel Hetterich, Walksat stalls well below satisfiability , SIAM Journal on Discrete Mathematics 31
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Wei-Kuo Chen and Arnab Sen, Parisi formula, disorder chaos and fluctuation for the ground state energy in the spherical mixed p p -spin models , Comm. Math. Phys. 350
2017
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Gamarnik David and Zadik Ilias, High dimensional regression with binary coefficients. estimating squared error and a phase transtition , Conference on Learning Theory, 2017, pp. 948–953
2017
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Wei-Kuo Chen, Madeline Handschy, and Gilad Lerman, On the energy landscape of the mixed even p-spin model , Probability Theory and Related Fields, 171
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David Gamarnik and Quan Li, Finding a large submatrix of a gaussian random matrix , The Annals of Statistics 46
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