ISBN: 0355670607 9780355670608

Category: Unavailable

Page count: 58

This paper demonstrates an introduction to the statistical distribution of eigenvalues in Random Matrix theory. Using mathematical analysis and probabilistic measure theory instead of statistical methods, we are able to draw conclusions on large dimensional cases and as our dimensions of the random matrices tend to infinity. Applications of large-dimensional random matrices occur in the study of heavy-nuclei atoms, where Eigenvalues express some physical measurement or observation at a distinct state of a quantum-mechanical system. This specifically motivates our study of Wigner Matrices. Classical limit theorems from statistics can fail in the large-dimensional case of a covariance matrix. By using methods from combinatorics and complex analysis, we are able to draw multiple conclusions on its spectral distributions. The Spectral distributions that arise allow for boundedness to occur on extreme eigenvalues.