A Note on Optimal Soft Edge Expansions for the Gaussian β Ensembles

2025/10/15 by Peter J. Forrester, Forrester, Peter J., Anas A. Rahman +3
Mathematics · #15B52 (Primary) #34C60 #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2510.13092

openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

We present some review material relating to the topic of optimal asymptotic expansions of correlation functions and associated observables for β ensembles in random matrix theory. We also give an introduction to a related line of study that we are presently undertaking.

Citations

• Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge II: Level Densities
• Dualities in random matrix theory
• Asymptotic Expansions of the Limit Laws of Gaussian and Laguerre (Wishart) Ensembles at the Soft Edge
• Asymptotic correlations for Gaussian and Wishart matrices with external source
• Generating functions for intersection numbers on moduli spaces of curves
• On the Distribution of the Roots of Certain Symmetric Matrices

Related

• Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge II: Level Densities
• Global spectrum fluctuations for Gaussian beta ensembles: a martingale approach
• Spiking the random matrix hard edge
• Operator level hard-to-soft transition for β-ensembles
• Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge III: Generating Functions