A Generalization of Random Matrix Ensemble I: General Theory

2005/02/06 by Jinpeng An, Zhengdong Wang, An, Jinpeng +3
Mathematics · Physics and Astronomy · #15A52 #57S25 #58C35 #Advanced Combinatorial Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Random Matrices and Applications #math-ph #math.MP #msc:15A52 #msc:57S25 #msc:58C35

paper · pdf · doi:10.48550/arxiv.math-ph/0502020

15 pages

arxiv created 2005/02/06 · openalex publication_date 2005/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a generalization of the random matrix ensembles, including all lassical ensembles. Then we derive the joint density function of the generalized ensemble by one simple formula, which give a direct and unified way to compute the density functions for all classical ensembles and various kinds of new ensembles. An integration formula associated with the generalized ensemble is also given. We also give a classification scheme of the generalized ensembles, which will include all classical ensembles and some new ensembles which were not considered before.

Citations

• A Generalization of Random Matrix Ensemble II: Concrete Examples and Integration Formulae
• A new classification scheme for Random Matrix Theories
• On the realization of Riemannian symmetric spaces in Lie groups

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