On the norm and eigenvalue distribution of large random matrices

DOI10.1214/aop/1022677390zbMath0941.15021OpenAlexW2087299215MaRDI QIDQ1807210

Anne Boutet de Monvel-Berthier, Alexei Khorunzhy

Publication date: 9 November 1999

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1022677390

zbMATH Keywords

normStieltjes transformlarge random matricesspectra of random matricesrandom operatorssymmetric random matriceseigenvalues distribution

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52) Convergence of probability measures (60B10)

Related Items

Local spectral statistics of Gaussian matrices with correlated entries, On the limiting spectral density of random matrices filled with stochastic processes, The limiting spectral distribution of the product of the Wigner matrix and a nonnegative definite matrix, The limiting spectral distribution in terms of spectral density, On the empirical spectral distribution for matrices with long memory and independent rows, From random matrices to long range dependence, On the universality of spectral limit for random matrices with martingale differences entries, On the limiting spectral distribution for a large class of symmetric random matrices with correlated entries

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Characteristic vectors of bordered matrices with infinite dimensions
• Necessary and sufficient conditions for almost sure convergence of the largest eigenvalue of a Wigner matrix
• A limit theorem for the norm of random matrices
• The triangle law for Lyapunov exponents of large random matrices
• Products of random matrices in statistical physics
• Level spacing distributions and the Bessel kernel
• On the statistical mechanics approach in the random matrix theory: Integrated density of states.
• Limits of infinite interaction radius, dimensionality and the number of components for random operators with off-diagonal randomness
• Large deviation principles for the Hopfield model and the Kac-Hopfield model
• On the norm of random matrices
• Free Random Variables
• Central limit theorem for traces of large random symmetric matrices with independent matrix elements
• Asymptotic properties of large random matrices with independent entries
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES