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We study here the so-called spiked Wigner and Wishart models, where one observes a low-rank matrix perturbed by some Gaussian noise.
Some inequalities satisfied by the quantities of information of fisher and shannon
Aart J Stam · 1959
Earlier work this paper cites.
Ordinary Differential Equations
Philip Hartman · 1964
Earlier work this paper cites.
Solution of’solvable model of a spin glass’
David J Thouless, Philip W Anderson, and Robert G Palmer · 1977
Earlier work this paper cites.
Random-energy model: Limit of a family of disordered models
Bernard Derrida · 1980
Earlier work this paper cites.
Random-energy model: An exactly solvable model of disordered systems
Bernard Derrida · 1981
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Spin glass theory and beyond: An Introduction to the Replica Method and Its Applications
Marc Mézard, Giorgio Parisi, and Miguel Virasoro · 1987
Earlier work this paper cites.
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Earlier work this paper cites.
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