Uniqueness of the Gaussian Orthogonal Ensemble
Probability
2019-10-02 v3
Abstract
A known result in random matrix theory states the following: Given a random Wigner matrix which belongs to the Gaussian Orthogonal Ensemble (GOE), then such matrix has an invariant distribution under orthogonal conjugations. The goal of this work is to prove the converse, that is, if is a symmetric random matrix such that it is invariant under orthogonal conjugations, then such matrix belongs to the GOE. We will prove this using some elementary properties of the characteristic function of random variables.
Keywords
Cite
@article{arxiv.1901.09257,
title = {Uniqueness of the Gaussian Orthogonal Ensemble},
author = {Jose Angel Sanchez Gomez and Victor Amaya Carvajal},
journal= {arXiv preprint arXiv:1901.09257},
year = {2019}
}