For products of bi-invariant random matrices over non-archimedean fields, singular numbers obey an SLLN and CLT with limits given by the corners, extending known type-A/type-C results to all split reductive groups.
Groupes r´ eductifs s ur un corps local: I
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Gaussian Universality of Products Over Split Reductive Groups and the Satake Isomorphism
For products of bi-invariant random matrices over non-archimedean fields, singular numbers obey an SLLN and CLT with limits given by the corners, extending known type-A/type-C results to all split reductive groups.