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Truncation of Haar random matrices in \(\mathrm{GL}_N(\mathbb{Z}_m)\). (English) Zbl 1385.60010
Summary: The asymptotic law of the truncated \(S\times S\) random submatrix of a Haar random matrix in \(\mathrm{GL}_N(\mathbb{Z}_m)\) as \(N\) goes to infinity is obtained. The same result is also obtained when \(\mathbb{Z}_m\) is replaced by any commutative compact local ring whose maximal ideal is topologically closed.
MSC:
60B20 Random matrices (probabilistic aspects)
15B52 Random matrices (algebraic aspects)
15B33 Matrices over special rings (quaternions, finite fields, etc.)
60B10 Convergence of probability measures
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