RANDOM TRUNCATIONS OF HAAR DISTRIBUTED MATRICES AND BRIDGES
type: Dataset
description: Let $U$ be a Haar distributed matrix in $\mathbb U(n)$ or $\mathbb O (n)$. In a previous paper, we proved that after centering, the two-parameter process \[T^{(n)} (s,t) = \sum_{i \leq \lfloor ns \rfloor, j \leq \lfloor nt\rfloor} |U_{ij}|^2\] converges in distribution to the bivariate tied-down Brownian bridge. 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 $n^{-1/2}$ converges to a Gaussian process. On the way we meet other interesting convergences.
landing page: https://hal.science/hal-00794540
keyword: 15b52-60f17-60j65
keyword: bivariate-brownian-bridge
keyword: infoeu-reposemanticspreprint
keyword: invariance-principle
keyword: mathmath-prmathematics-mathprobability-mathpr
keyword: orthogonal-ensemble
keyword: preprints-working-papers-
keyword: random-matrices
keyword: unitary-ensemble
issued: 2026-05-14T03:45:15.311966
modified: 2026-05-14T03:45:15.311974
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

RANDOM TRUNCATIONS OF HAAR DISTRIBUTED MATRICES AND BRIDGES
type: Distribution
format: HTML
access URL: https://hal.science/hal-00794540
issued: 2026-05-14T03:45:15.337806
modified: 2026-05-14T03:45:15.255344