Finite Size Effects for Spacing Distributions in Random Matrix Theory: Circular Ensembles and Riemann Zeros

DOI10.1111/sapm.12160zbMath1368.81080arXiv1608.04638OpenAlexW2963383941MaRDI QIDQ5281638

Anthony Mays, Folkmar A. Bornemann, Peter J. Forrester

Publication date: 26 July 2017

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.04638

Mathematics Subject Classification ID

Quantum chaos (81Q50) Perturbation theories for operators and differential equations in quantum theory (81Q15) Random matrices (algebraic aspects) (15B52) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

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Cites Work

• Unnamed Item
• Unnamed Item
• Singular values and evenness symmetry in random matrix theory
• Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
• Algebraic aspects of increasing subsequences
• A method for calculating spectral statistics based on random-matrix universality with an application to the three-point correlations of the Riemann zeros
• Iteration-Free Computation of Gauss--Legendre Quadrature Nodes and Weights
• Statistical Theory of the Energy Levels of Complex Systems. I
• Evenness symmetry and inter-relationships between gap probabilities in random matrix theory
• On the numerical evaluation of Fredholm determinants
• On the statistical properties of the level-spacings in nuclear spectra
• Sur la loi limite de l'espacement des valeurs propres d'une matrice ale´atoire
• Proof of a Conjecture by Dyson in the Statistical Theory of Energy Levels
• Zeroes of zeta functions and symmetry
• The Riemann Zeros and Eigenvalue Asymptotics
• The Jacobi polynomial ensemble and the Painlevé VI equation
• On the Distribution of Spacings Between Zeros of the Zeta Function
• Application of theτ-function theory of Painlevé equations to random matrices:P_VI, the JUE, CyUE, cJUE and scaled limits
• On the Numerical Evaluation of Distributions in Random Matrix Theory: A Review
• Gutzwiller's Trace Formula and Spectral Statistics: Beyond the Diagonal Approximation
• Statistical Theory of the Energy Levels of Complex Systems. V
• The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics
• Finite-size corrections in random matrix theory and Odlyzko’s dataset for the Riemann zeros
• Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
• Statistical Analysis and Modelling of Spatial Point Patterns
• On the spacing distribution of the Riemann zeros: corrections to the asymptotic result
• Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles
• Random matrix theory and \(\zeta(1/2+it)\).