Nested beta-Laguerre ensembles

Reversal and transposition of the Dumitriu–Edelman bidiagonal model give one infinite Jacobi matrix whose leading blocks have beta-Laguerre spectra at every size, with any fixed integrable hard-edge power. This elementary consequence of the finite model gives a positive Laguerre answer to Virág's question about nested ensembles. The antisymmetric Gaussian beta family admits the same kind of coupling. We distinguish these constructions from full corners processes and operator-limit couplings, and prove several obstructions under specified spectral-weight, independence, or principal-block assumptions.