For broad classes of random p-adic polynomials and matrices, limiting root and eigenvalue-factor statistics match the Haar coefficient model.
Bulk universality for generalized Wigner matrices.Probability Theory and Related Fields, 154(1-2):341–407, 2012
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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.