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We prove that the two point correlation matrix $ \textbf{M}= (\langle \sigma_i ; \sigma_j\rangle)_{1\leq i,j\leq N} \in \mathbb{R}^{N\times N}$ of the Sherrington-Kirkpatrick model has the property that for every $\epsilon>0$ there exists $K_\epsilon>0$, that is independent of $N$, such that \[ \mathbb{P}\big( \| \textbf{M} \|_{\text{op}} \leq K_{\epsilon}\big) \geq 1- \epsilon \] for $N$ large enough, for suitable interaction and external field parameters $(\beta,h)$ in the replica symmetric region.
Gaussian random processes and measures of solid angles in hilbert space
V. N. Sudakov · 1971
Earlier work this paper cites.
Regularité des trajectoires des fonctions aléatoires gaussiennes
X. Fernique · 1975
Earlier work this paper cites.
Solvable model of a spin glass
D. Sherrington and S. Kirkpatrick · 1975
Earlier work this paper cites.
Solution of ’solvable model in spin glasses’
P. W. Anderson, , R. G. Palmer, and D. J. Thouless · 1977
Earlier work this paper cites.
Stability of the Sherrington-Kirkpatrick solution of a spin glass model
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Earlier work this paper cites.
Geometric Problems in the Theory of Infinite-Dimensional Probability Distributions
V. N. Sudakov · 1979
Earlier work this paper cites.
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T. Plefka · 1982
Earlier work this paper cites.
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Mean Field Models for Spin Glasses: Volume I: Basic Examples
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