The probability distribution of spectral moments for the Gaussian beta-ensembles

Abstract

We derive the joint probability distribution of the first two spectral moments for the G$\beta$E random matrix ensembles in N dimensions for any N. This is achieved by making use of two complementary invariants of the domain in ${\mathbb{R}}^N$ where the spectral moments are defined. Our approach is significantly different from those employed previously to answer related questions and potentially offers new insights. We also discuss the problems faced when attempting to include higher spectral moments.

13 pages

References in corpus (3)

• On invariant 2x2 β-ensembles of random matrices
• Dyson's Brownian-motion model for random matrix theory - revisited. With an Appendix by Don Zagier
• Linear statistics of the circular $\beta$-ensemble, Stein's method, and circular Dyson Brownian motion

Cited by in corpus (2)

• Linear statistics and pushed Coulomb gas at the edge of beta random matrices: four paths to large deviations
• Spectral statistics of the uni-modular ensemble