2016/05/22 by Takashi Shinzato, Shinzato, Takashi
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Economics and business #FOS: Physical sciences #Graph theory and applications #Mathematical Physics (math-ph) #Opinion Dynamics and Social Influence #Portfolio Management (q-fin.PM) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1605.06840
openalex publication_date 2016/05/22 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
In the present work, eigenvalue distributions defined by a random rectangular\nmatrix whose components are neither independently nor identically distributed\nare analyzed using replica analysis and belief propagation. In particular, we\nconsider the case in which the components are independently but not identically\ndistributed; for example, only the components in each row or in each column may\nbe identically distributed. We also consider the more general case in which\nthe components are correlated with one another. We use the replica approach\nwhile making only weak assumptions in order to determine the asymptotic\neigenvalue distribution and to derive an algorithm for doing so, based on\nbelief propagation. One of our findings supports the results obtained from\nFeynman diagrams. We present the results of several numerical experiments that\nvalidate our proposed methods.\n