Abstract
Matrices with random matrix elements appear to have applications in physics, mathematics, biology, telecommunications, etc. In fact, experimental data of many complex systems, such as the spacing distribution of energy level spectra of heavy nuclei, and the distribution of the nonreal zeros of the Riemann zeta function can be reproduced using the theory of such matrices. In this article, we present the integral calculus of matrices with random matrix elements which will provide the necessary foundation to study their applications. In particular, we will present in detail an elegant and systematic tool called Feynman’s method to perform integration of matrices.
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