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Statistics of spectral properties of matrix-valued random variables.

49 votes

Expected determinant of a random NxN matrix

If $N \ge 2$, then the expected value is $0$ since interchanging two rows preserves the distribution but negates the determinant.
Bjorn Poonen's user avatar
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distribution of degree of minimum polynomial for eigenvalues of random matrix with elements ...

The survey article Jason Fulman, Random matrix theory over finite fields, Bulletin of the AMS 39 (2002), 51-85 and the references therein should answer your questions to the extent that the answers …
Bjorn Poonen's user avatar
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