The joint distribution of singular numbers of all principal corners of a Haar-random p-adic Hermitian or alternating matrix is a (formal) Hall-Littlewood process.
Modeling the distribution of ranks, S elmer groups, and S hafarevich-- T ate groups of elliptic curves
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Non-Archimedean GUE corners and Hecke modules
The joint distribution of singular numbers of all principal corners of a Haar-random p-adic Hermitian or alternating matrix is a (formal) Hall-Littlewood process.