2003/06/12 by Pierluigi Contucci, Sandro Graffi
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Random Matrices and Applications #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1142/s0217979204024203
11 pages
arxiv created 2003/06/12 · openalex publication_date 2004/02/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Consider a correlated Gaussian random energy model built by successively adding one particle (spin) into the system and imposing the positivity of the associated covariance matrix. We show that the validity of a recently isolated condition ensuring the existence of the thermodynamic limit forces the covariance matrix to exhibit the Parisi replica symmetry breaking scheme with a convexity conditions on the matrix elements.