Spacings: An Example for Universality in Random Matrix Theory

2013/01/01 by Thomas Kriecherbauer, Kristina Schubert · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Bayesian Methods and Mixture Models #Eigenvalues and eigenvectors #Mathematics #Physics #Pure mathematics #Quantum mechanics #Random Matrices and Applications #Random matrix #Sketch #Statistical physics #Stochastic processes and statistical mechanics #Symplectic geometry #Universality (dynamical systems) #math-ph #math.MP #math.PR

paper · pdf · doi:10.1007/978-3-642-38806-4_3

published in Springer proceedings in mathematics & statistics, 45-71 (Springer International Publishing) · reference [4] updated

openalex publication_date 2013/01/01 · arxiv created 2015/10/27 · arxiv updated 2015/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Universality of local eigenvalue statistics is one of the most striking phenomena of Random Matrix Theory, that also accounts for a lot of the attention that the field has attracted over the past 15 years. In this paper we focus on the empirical spacing distribution and its Kolmogorov distance from the universal limit. We describe new results, some analytical, some numerical, that are contained in [27]. A large part of the paper is devoted to explain basic definitions and facts of Random Matrix Theory, culminating in a sketch of the proof of a weak version of convergence for the empirical spacing distribution σ_N.

Citations

• Correlation Functions, Cluster Functions, and Spacing Distributions for Random Matrices
• Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles
• THE GENERALISED PRODUCT MOMENT DISTRIBUTION IN SAMPLES FROM A NORMAL MULTIVARIATE POPULATION
• Random matrices: Universality of local eigenvalue statistics