Abstract
We develop a tool to approximate the entries of a large dimensional complex Jacobi ensemble with independent complex Gaussian random variables. Based on this and the author's earlier work in this direction, we obtain the Tracy-Widom law of the largest singular values of the Jacobi emsemble. Moreover, the circular law, the Marchenko-Pastur law, the central limit theorem, and the laws of large numbers for the spectral norms are also obtained.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 221-246 |
| Number of pages | 26 |
| Journal | Probability Theory and Related Fields |
| Volume | 144 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - May 2009 |
Bibliographical note
Funding Information:Supported in part by NSF #DMS-0449365.
Keywords
- Eigenvalue
- Empirical distribution
- Haar measure
- Largest eigenvalue
- Limiting distribution
- Random matrix
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