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We argue that Hamilton-Jacobi equations provide a convenient and intuitive approach for studying the large-scale behavior of mean-field disordered systems.
Spin glass theory and beyond: an introduction to the replica method and its applications
M. Mézard, G. Parisi, and M. Virasoro · 1987
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User’s guide to viscosity solutions of second order partial differential equations
M. G. Crandall, H. Ishii, and P.-L. Lions · 1992
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Broken replica symmetry bounds in the mean field spin glass model
F. Guerra · 2003
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The Parisi formula
M. Talagrand · 2006
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Mean field models for spin glasses: some obnoxious problems
M. Talagrand · 2007
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A simple proof of the Poincaré inequality for a large class of probability measures including the log-concave case
D. Bakry, F. Barthe, P. Cattiaux, and A. Guillin · 2008
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Replica symmetry breaking in mean-field spin glasses through the Hamilton-Jacobi technique
A. Barra, A. Di Biasio, and F. Guerra · 2010
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Partial differential equations
L. C. Evans · 2010
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Mean field models for spin glasses. Volume II
M. Talagrand · 2011
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Mean field spin glasses treated with PDE techniques
A. Barra, G. Del Ferraro, and D. Tantari · 2013
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Concentration inequalities
S. Boucheron, G. Lugosi, and P. Massart · 2013
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The Sherrington-Kirkpatrick model
D. Panchenko · 2013
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Superconcentration and related topics
S. Chatterjee · 2014
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Information-theoretically optimal sparse PCA
Y. Deshpande and A. Montanari · 2014
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Phase transitions in sparse PCA
T. Lesieur, F. Krzakala, and L. Zdeborová · 2015
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Mutual information for symmetric rank-one matrix estimation: a proof of the replica formula
J. Barbier, M. Dia, N. Macris, F. Krzakala, T. Lesieur, and L. Zdeborová · 2016
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The layered structure of tensor estimation and its mutual information
J. Barbier, N. Macris, and L. Miolane · 2017
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Statistical and computational phase transitions in spiked tensor estimation
T. Lesieur, L. Miolane, M. Lelarge, F. Krzakala, and L. Zdeborová · 2017
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The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference
J. Barbier and N. Macris
Cited in the paper.
A. El Alaoui and F. Krzakala
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Fundamental limits of symmetric low-rank matrix estimation
M. Lelarge and L. Miolane
Cited in the paper.