Perturbed Laguerre unitary ensembles, Hankel determinants, and information theory

DOI10.1002/mma.3399zbMath1357.94046OpenAlexW1775520997MaRDI QIDQ2795253

Yang Chen, Estelle L. Basor

Publication date: 18 March 2016

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.3399

zbMATH Keywords

Hankel determinantintegral representationsmoment generating functionoutage probabilityperturbed Laguerre weightinformation-theoretic performance metricmultiple-antenna wireless communications

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Random matrices (algebraic aspects) (15B52) Information theory (general) (94A15) Painlevé-type functions (33E17)

Related Items

The Hankel determinant associated with a singularly perturbed Laguerre unitary ensemble, On a distinguished family of random variables and Painlevé equations, Critical edge behavior in the perturbed Laguerre unitary ensemble and the Painlevé V transcendent, Painlevé V, Painlevé XXXIV and the degenerate Laguerre unitary ensemble, Painlevé V and confluent Heun equations associated with a perturbed Gaussian unitary ensemble, Hankel determinant and orthogonal polynomials for a perturbed Gaussian weight: From finite n to large n asymptotics, Single-user MIMO system, Painlevé transcendents, and double scaling, Character expansion of matrix integrals, Exceptional solutions to the Painlevé VI equation associated with the generalized Jacobi weight, Orthogonal polynomials, asymptotics, and Heun equations, Singular linear statistics of the Laguerre unitary ensemble and Painlevé. III. Double scaling analysis

Cites Work

• Unnamed Item
• A Mathematical Theory of Communication
• The Hilbert series of \(\mathcal{N}=1\) \(SO(N_c)\) and \(Sp(N_c)\) SQCD, Painlevé VI and integrable systems
• The Hilbert series of U/SU SQCD and Toeplitz determinants
• Correlations of RMT characteristic polynomials and integrability: Hermitean matrices
• Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
• Level-spacing distributions and the Airy kernel
• Fredholm determinants, differential equations and matrix models
• Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials
• Painlevé III and a singular linear statistics in Hermitian random matrix ensembles. I.
• PDEs SATISFIED BY EXTREME EIGENVALUES DISTRIBUTIONS OF GUE AND LUE
• Painlevé functions of the third kind
• Coulumb Fluid, Painlevé Transcendents, and the Information Theory of MIMO Systems
• THE DISTRIBUTION OF THE FIRST EIGENVALUE SPACING AT THE HARD EDGE OF THE LAGUERRE UNITARY ENSEMBLE
• Painlevé V and time-dependent Jacobi polynomials