On the condition number of the critically-scaled Laguerre unitary ensemble

DOI10.3934/dcds.2016.36.4287zbMath1335.60008arXiv1507.00750OpenAlexW2964328606MaRDI QIDQ262100

Thomas Trogdon, Percy A. Deift, Govind K. Menon

Publication date: 29 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.00750

zbMATH Keywords

conjugate gradient algorithmLaguerre polynomialsRiemann-Hilbert problemsLaguerre unitary ensembleWishart ensemble

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items

A note on spiked Wishart matrices, Universality for the Conjugate Gradient and MINRES Algorithms on Sample Covariance Matrices, Universality for Eigenvalue Algorithms on Sample Covariance Matrices, Universal halting times in optimization and machine learning, The conjugate gradient algorithm on well-conditioned Wishart matrices is almost deterministic, The random matrix hard edge: rare events and a transition, Some open problems in random matrix theory and the theory of integrable systems. II, Operator level hard-to-soft transition for \(\beta\)-ensembles, Smoothed analysis for the conjugate gradient algorithm

Uses Software

• DLMF
• numericaluniversality

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Critical edge behavior and the Bessel to Airy transition in the singularly perturbed Laguerre unitary ensemble
• Strong asymptotics of Laguerre-type orthogonal polynomials and applications in random matrix theory
• Approximation of rectangular beta-Laguerre ensembles and large deviations
• Global asymptotic expansions of the Laguerre polynomials -- a Riemann-Hilbert approach
• Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences
• The isomonodromy approach to matrix models in 2D quantum gravity
• Level-spacing distributions and the Airy kernel
• On the exact distribution of the smallest root of the Wishart matrix using zonal polynomials
• On the distribution of the largest eigenvalue in principal components analysis
• The Riemann--Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]
• The spectrum edge of random matrix ensembles.
• Shape fluctuations and random matrices
• PDEs SATISFIED BY EXTREME EIGENVALUES DISTRIBUTIONS OF GUE AND LUE
• Universality in numerical computations with random data
• Eigenvalues and Condition Numbers of Random Matrices
• Random matrix ensembles with an effective extensive external charge
• On the Distribution of the Largest Latent Root and the Corresponding Latent Vector for Principal Component Analysis
• Estimates for Some Computational Techniques in Linear Algebra
• DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
• Numerical Inverting of Matrices of High Order. II
• Methods of conjugate gradients for solving linear systems