| Popis: |
This paper demonstrates an introduction to the statistical distribution of eigenval-ues in Random Matrix theory. Using mathematical analysis and probabilistic measuretheory instead of statistical methods, we are able to draw conclusions on large dimen-sional cases and as our dimensions of the random matrices tend to innity. Applicationsof large-dimensional random matrices occur in the study of heavy-nuclei atoms, whereEigenvalues express some physical measurement or observation at a distinct state ofa quantum-mechanical system. This specically motivates our study of Wigner Ma-trices. Classical limit theorems from statistics can fail in the large-dimensional caseof a covariance matrix. By using methods from combinatorics and complex analysis,we are able to draw multiple conclusions on its spectral distributions. The Spectraldistributions that arise allow for boundedness to occur on extreme eigenvalues. |
