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The Wigner spiked model in a mismatched setting is studied with the finite temperature Statistical Mechanics approach through its representation as a Sherrington-Kirkpatrick model with added Mattis interaction.
“Spin Glass Theory and Beyond”, Lecture Notes in Physics Series
M. Mezard, G. Parisi and M.A. Virasoro · 1987
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“About The Overlap Distribution In Mean Field Spin Glass Models”
Francesco Guerra · 1997
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“On Ruelle’s Probability Cascades and an Abstract Cavity Method”
E. Bolthausen and A.-S. Sznitman · 1998
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“Statistical Physics of Spin Glasses and Information Processing: an Introduction”
Hidetoshi Nishimori · 2001
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“The Thermodynamic Limit in Mean Field Spin Glass Models”
Francesco Guerra and Fabio Toninelli · 2002
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“About the Almeida-Thouless transition line in the Sherrington-Kirkpatrick mean-field spin glass model”
F. Toninelli · 2002
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“Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model”
Francesco Guerra · 2003
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“Griffiths inequalities for the Gaussian spin glass”
Satoshi Morita, Hidetoshi Nishimori and Pierluigi Contucci · 2004
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“The Ghirlanda-Guerra Identities”
Pierluigi Contucci and Cristian Giardina · 2005
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“Surface Terms on the Nishimori Line of the Gaussian Edwards-Anderson Model”
Pierluigi Contucci, Satoshi Morita and Hidetoshi Nishimori · 2005
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“Entropy, Large Deviations, and Statistical Mechanics”
Richard Ellis · 2006
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“The Parisi Formula”
Michel Talagrand · 2006
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“Spin Glass Computations and Ruelle’s Probability Cascades”
Louis-Pierre Arguin · 2007
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“On differentiability of the Parisi formula”
Dmitry Panchenko · 2007
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“A mechanical approach to mean field spin models”
Giuseppe Genovese and Adriano Barra · 2008
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“Strong replica symmetry for high-dimensional disordered log-concave Gibbs measures”, 2020
Jean Barbier, Dmitry Panchenko and Manuel Sáenz · 2009
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“Random Overlap Structures: Properties and Applications to Spin Glasses”
Louis-Pierre Arguin and Sourav Chatterjee · 2010
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“Tight Bounds on the Capacity of Binary Input Random CDMA Systems”
Satish Korada and Nicolas Macris · 2010
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“Mean Field Models for Spin Glasses: Volume I: Basic Examples”
Michel Talagrand · 2010
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“Mismatched Estimation and Relative Entropy”
Sergio Verdú · 2010
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“Mean Field Models for Spin Glasses: Volume II: Advanced Replica-Symmetry and Low Temperature”
Michel Talagrand · 2011
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“On the equivalence of Hopfield Networks and Boltzmann Machines”
Adriano Barra, Alberto Bernacchia, Enrica Santucci and Pierluigi Contucci · 2012
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“An Iterative Construction of Solutions of the TAP Equations for the Sherrington-Kirkpatrick Model”
Erwin Bolthausen · 2012
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“Perspectives on Spin Glasses”
Pierluigi Contucci and Cristian Giardinà · 2012
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“Iterative estimation of constrained rank-one matrices in noise”
Sundeep Rangan and Alyson. Fletcher · 2012
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“The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference”
Jean Barbier and Nicolas Macris · 2019
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“Neural networks with a redundant representation: detecting the undetectable”
E. Agliari, F. Alemanno, A. Barra, M. Centonze and A. Fachechi · 2020
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“Tolerance versus synaptic noise in dense associative memories”
E. Agliari and G. Marzo · 2020
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“Fundamental limits of detection in the spiked Wigner model”
Ahmed El-alaoui, Florent Krzakala and Michael Jordan · 2020
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“The multi-species mean-field spin-glass on the Nishimori line”
Diego Alberici, Francesco Camilli, Pierluigi Contucci and Emanuele Mingione · 2020
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“Overlap matrix concentration in optimal Bayesian inference”
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“On the mixed even-spin Sherrington-Kirkpatrick model with ferromagnetic interaction”
Wei Kuo Chen · 2014
Cited alongside, same era.
“On properties of Parisi measures”
A. Auffinger and Wei-Kuo Chen · 2015
Cited alongside, same era.
“The Parisi Formula has a Unique Minimizer”
A. Auffinger and Wei-Kuo Chen · 2015
Cited alongside, same era.
“The Sherrington-Kirkpatrick Model”
Dmitry Panchenko · 2015
Cited alongside, same era.
“Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula”
Jean Barbier, Mohamad Dia, Nicolas Macris, Florent Krzakala, Thibault Lesieur and Lenka Zdeborová · 2016
Cited alongside, same era.
“Mean-field message-passing equations in the Hopfield model and its generalizations”
Marc Mézard · 2016
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Jean Barbier · 2020
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“Strong replica symmetry in high-dimensional optimal Bayesian inference”
Jean Barbier and Dmitry Panchenko · 2020
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“Information-theoretic limits of a multiview low-rank symmetric spiked matrix model”
Jean Barbier and Galen Reeves · 2020
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“High-dimensional rank-one nonsymmetric matrix decomposition: the spherical case”
Clément Luneau, N. Macris and Jean Barbier · 2020
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“Hamilton–Jacobi equations for finite-rank matrix inference”
J.-C. Mourrat · 2020
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“Extending the Parisi formula along a Hamilton-Jacobi equation”
Jean-Christophe Mourrat and Dmitry Panchenko · 2020
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“Information-Theoretic Limits for the Matrix Tensor Product”
Galen Reeves · 2020
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“The solution of the deep Boltzmann machine on the Nishimori line”
Diego Alberici, Francesco Camilli, Pierluigi Contucci and Emanuele Mingione · 2021
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“Performance of Bayesian linear regression in a model with mismatch”, 2021
Jean Barbier, Wei-Kuo Chen, Dmitry Panchenko and Manuel Sáenz · 2021
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“Statistical inference of finite-rank tensors”
Hong-Bin Chen, Jean-Christophe Mourrat and Jiaming Xia · 2021
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“On the Almeida-Thouless transition line in the SK model with centered Gaussian external field”
Wei-Kuo Chen · 2021
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“Variational Inference in high-dimensional linear regression”, 2021
Sumit Mukherjee and Subhabrata Sen · 2021
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“Mismatched Estimation of rank-one symmetric matrices under Gaussian noise”, 2021
Farzad Pourkamali and Nicolas Macris · 2021
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