# Truncations of Haar distributed matrices, traces and bivariate Brownian bridges.

Abstract : Let U be a Haar distributed unitary matrix in U(n)or O(n). We show that after centering the double index process $W^{(n)} (s,t) = \sum_{i \leq \lfloor ns \rfloor, j \leq \lfloor nt\rfloor} |U_{ij}|^2$ converges in distribution to the bivariate tied-down Brownian bridge. The proof relies on the notion of second order freeness.
Keywords :
Document type :
Journal articles
Random matrices: theory and Applications (RMTA), 2011, 23 p. <10.1142/S2010326311500079>
Domain :
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00498758
Contributor : Catherine Donati-Martin <>
Submitted on : Monday, September 19, 2011 - 10:35:20 AM
Last modification on : Thursday, April 27, 2017 - 9:45:52 AM

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### Citation

Catherine Donati-Martin, Alain Rouault. Truncations of Haar distributed matrices, traces and bivariate Brownian bridges.. Random matrices: theory and Applications (RMTA), 2011, 23 p. <10.1142/S2010326311500079>. <hal-00498758v4>

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