Universal singularity at the closure of a gap in a random matrix theory

1998/04/01 by E. Brézin, E. Brezin, S. Hikami · 3 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Random Matrices and Applications #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.57.4140

20pages, Revtex, to be published in Phys. Rev. E

openalex publication_date 1998/04/01 · arxiv created 1998/04/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider a Hamiltonian H=H₀+V, in which H₀ is a given nonrandom Hermitian matrix, and V is an N\ifmmode×\else\texttimes\fiN Hermitian random matrix with a Gaussian probability distribution. We had shown before that Dyson's universality of the short-range correlations between energy levels holds at generic points of the spectrum independently of H₀. We consider here the case in which the spectrum of H₀ is such that there is a gap in the average density of eigenvalues of H which is thus split into two pieces. When the spectrum of H₀ is tuned so that the gap closes, a new class of universality appears for the energy correlations in the vicinity of this singular point.

Citations

• Spectral form factor in a random matrix theory
• Fredholm determinants, differential equations and matrix models
• Extension of level-spacing universality

Cited by

• Noncolliding Brownian Motion and Determinantal Processes
• Large n Limit of Gaussian Random Matrices with External Source, Part III: Double Scaling Limit
• Large n Limit of Gaussian Random Matrices with External Source, Part II