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Estimates for moments of random matrices with Gaussian elements
| Content Provider | Semantic Scholar |
|---|---|
| Author | Khorunzhiy, Oleksiy |
| Copyright Year | 2008 |
| Abstract | We describe an elementary method to get non-asymptotic estimates for the moments of Hermitian random matrices whose elements are Gaussian independent random variables. We derive a system of recurrent relations for the moments and the covariance terms and develop a triangular scheme to prove the recurrent estimates. The estimates we obtain are asymptotically exact in the sense that they give exact expressions for the first terms of 1/N-expansions of the moments and covariance terms. As the basic example, we consider the Gaussian Unitary Ensemble of random matrices (GUE). Immediate applications include the Gaussian Orthogonal Ensemble and the ensemble of Gaussian anti-symmetric Hermitian matrices. Finally we apply our method to the ensemble of N × N Gaussian Hermitian random matrices H (N,b) whose elements are zero outside of the band of width b. The other elements are taken from GUE; the matrix obtained is renormalized by b −1/2. We derive the estimates for the moments of H (N,b) and prove that the spectral norm H (N,b) remains bounded in the limit N, b → ∞ when (log N) 3/2 /b → 0. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math-ph/0507060v4.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math-ph/0507060v2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math-ph/0507060v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math-ph/0507060v5.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math-ph/0507060v3.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Emoticon Estimated Normal Statistical Distribution The Matrix width |
| Content Type | Text |
| Resource Type | Article |
