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The determinant of random power series matrices over finite fields. (English) Zbl 0964.15016
The set $$M_{n\times n}(F_q[[x]])$$ of $$n\times n$$-matrices $$A$$ with elements $$a_{ij}= \sum a_{ijt} x^t\in\mathbb F_q[[x]]$$ $$(t\geq 0)$$ is considered where $$\mathbb F_q[[x]]$$ denotes the ring of formal power series over the finite field $$\mathbb F_q$$ of $$q$$ elements. The probability distribution is studied of the coefficient $$d_t$$ of the determinant $$\det(A)= \sum d_tx^t$$ $$(t\geq 0)$$ if $$A$$ is random, i.e. if the coefficients of the entries of $$A$$ are statistically independent and uniform over the elements of the finite field $$\mathbb F_q$$.

##### MSC:
 15A15 Determinants, permanents, traces, other special matrix functions 60C05 Combinatorial probability 15B33 Matrices over special rings (quaternions, finite fields, etc.)
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##### References:
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