Random Truncations of Haar Distributed Matrices and Bridges
نویسنده
چکیده
Let U be a Haar distributed matrix in U(n) or O(n). In a previous paper, we proved that after centering, the two-parameter process T (s, t) = ∑ i≤⌊ns⌋,j≤⌊nt⌋ |Uij | 2 converges in distribution to the bivariate tied-down Brownian bridge. In the present paper, we replace the deterministic truncation of U by a random one, where each row (resp. column) is chosen with probability s (resp. t) independently. We prove that the corresponding two-parameter process, after centering and normalization by n converges to a Gaussian process. On the way we meet other interesting convergences.
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