Communications in Mathematical Physics

, Volume 252, Issue 1–3, pp 149–166 | Cite as

On the Moments of Traces of Matrices of Classical Groups

  • L. PasturEmail author
  • V. Vasilchuk


We consider random matrices, belonging to the groups U(n), O(n) , SO(n), and Sp(n) and distributed according to the corresponding unit Haar measure. We prove that the moments of traces of powers of the matrices coincide with the moments of certain Gaussian random variables if the order of moments is low enough. Corresponding formulas, proved partly before by various methods, are obtained here in the framework of a unique method, reminiscent of the method of correlation equations of statistical mechanics. The equations are derived by using a version of the integration by parts.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Statistical Mechanic 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.University Paris 7ParisFrance
  2. 2.Institute for Low Temperature PhysicsKharkivUkraine

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