For broad classes of random p-adic polynomials and matrices, limiting root and eigenvalue-factor statistics match the Haar coefficient model.
How many zeros of a random polynomial are real?Bulletin of the American Mathematical Society, 32(1):1–37, 1995
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Universality for Random $p$-adic Polynomials and Random Matrices Via the Resultant Distribution Method
For broad classes of random p-adic polynomials and matrices, limiting root and eigenvalue-factor statistics match the Haar coefficient model.