Truncations of Haar distributed matrices, traces and bivariate Brownian bridges
نویسندگان
چکیده
Let U be a Haar distributed matrix in U(n) or O(n). We show that after centering the two-parameter process W (s, t) = ∑ i≤⌊ns⌋,j≤⌊nt⌋ |Uij | 2 converges in distribution to the bivariate tied-down Brownian bridge.
منابع مشابه
Truncations of Haar Distributed Matrices, Traces and Bivariate Brownian Bridge
Let U be a Haar distributed matrix in U(n) or O(n). We show that after centering the two-parameter process W (s, t) = ∑ i≤⌊ns⌋,j≤⌊nt⌋ |Uij | 2 converges in distribution to the bivariate tied-down Brownian bridge.
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