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Matrix Models for Beta Ensembles

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arxiv math-ph/0206043 v1 pith:SRBBOJXU submitted 2002-06-25 math-ph math.MPmath.PRmath.RT

Ioana Dumitriu , Alan Edelman This is my paper · ORCID
classification math-phmath.MPmath.PRmath.RT
keywords betamodelsensemblesmatrixgaussianlaguerrewishartapplications
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abstract

This paper constructs tridiagonal random matrix models for general ($\beta>0$) $\beta$-Hermite (Gaussian) and $\beta$-Laguerre (Wishart) ensembles. These generalize the well-known Gaussian and Wishart models for $\beta = 1,2,4$. Furthermore, in the cases of the $\beta$-Laguerre ensembles, we eliminate the exponent quantization present in the previously known models. We further discuss applications for the new matrix models, and present some open problems.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 481 citations worldwide. Full citation record

  1. Logarithmic Spectral Distribution of a Non-Hermitian $\beta$-Ensemble

    math-ph 2025-04 unverdicted novelty 7.0 of 10

    The limiting spectral density of the new non-Hermitian beta-ensemble is the logarithm of the radius plus a constant, rotationally invariant on a compact disk.

  2. Controlled Chaos in 4D SCFTs

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    Orbifolds of N=4 SYM produce SCFTs whose dilatation operator in a subsector is realized by a tunable spin chain whose eigenvalue statistics exhibit chaos for specific marginal couplings.

  3. Higher-dimensional chaotic features and random matrix signatures following a local quench

    hep-th 2026-07 conditional novelty 5.0 of 10

    Extrema of local-quench two-point functions in free 1+1 and 2+1 scalar theory show soft-to-GOE nearest-neighbor repulsion and geometry-dominated all-pair form factors.

  4. Higher-Order Krylov State Complexity in Random Matrix Quenches

    hep-th 2024-12 conditional novelty 5.0 of 10

    Higher-order generalized spread complexities show a more pronounced pre-equilibration peak than standard spread complexity in random matrix quenches, quantifying chaos more sharply up to third order.

  5. Krylov Complexity

    hep-th 2025-07 unverdicted novelty 2.0 of 10

    Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.

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