Remarks on the interpolation method

Abstract

We discuss a generalization of the conditions of validity of the interpolation method for the density of quenched free energy of mean field spin glasses. The condition is written just in terms of the $L^2$ metric structure of the Gaussian random variables. As an example of application we deduce the existence of the thermodynamic limit for a GREM model with infinite branches for which the classic conditions of validity fail.

arXiv comment20 pages, 4 figures

References in corpus (8)

• Euclidean Distance Matrices: Essential Theory, Algorithms and Applications
• The Thermodynamic Limit in Mean Field Spin Glass Models
• The Mutual Information in Random Linear Estimation
• The mean field Ising model trough interpolating techniques
• Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation
• A note on classical ground state energies
• An error bound in the Sudakov-Fernique inequality
• Thermodynamical Limit for Correlated Gaussian Random Energy Models