Abstract
Let Γn=(γij)n×n be a random matrix with the Haar probability measure on the orthogonal group O(n), the unitary group U(n), or the symplectic group Sp(n). Given 1≤m < n, a probability inequality for a distance between (γij)n×m and some mn independent F-valued normal random variables is obtained, where F=ℝ, ℂ, or ℍ (the set of real quaternions). The result is universal for the three cases. In particular, the inequality for Sp(n) is new.
Original language | English (US) |
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Pages (from-to) | 1227-1243 |
Number of pages | 17 |
Journal | Journal of Theoretical Probability |
Volume | 23 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2010 |
Bibliographical note
Funding Information:Supported in part by NSF#DMS-0449365.
Keywords
- Classical compact group
- Gaussian distribution
- Haar measure
- Independence
- Probability inequality
- Random matrix