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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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