Truncations of Haar distributed matrices, traces and bivariate Brownian bridges (Q2893156)
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scientific article; zbMATH DE number 6049963
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Truncations of Haar distributed matrices, traces and bivariate Brownian bridges |
scientific article; zbMATH DE number 6049963 |
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26 June 2012
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random matrices
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unitary ensemble
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orthogonal ensemble
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bivariate Brownian bridge
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invariance principle
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Truncations of Haar distributed matrices, traces and bivariate Brownian bridges (English)
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If \(U\) is a Haar distributed matrix in the set of the unitary or orthogonal matrices, the authors show that after centering the two-parametric process NEWLINE\[NEWLINEW^{( n )} ( x, t ) = \sum_{i \leq [ns] j \leq [nt]} | U_{ij} |^2,NEWLINE\]NEWLINE converges in distribution to the bivariate tied-down Brownian bridge.
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