Asymptotic analysis of the density of states in random matrix models associated with a slowly decaying weight

DOI10.1016/S0377-0427(00)00638-5zbMath1009.42015OpenAlexW2093898987MaRDI QIDQ5946587

Arno B. J. Kuijlaars

Publication date: 14 October 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(00)00638-5

zbMATH Keywords

asymptoticsorthogonal polynomialsrandom matricesdensity of stateslogarithmic potentialsslowly decaying weightStieltjes-Wigert polynomialsweak limit

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random matrices (algebraic aspects) (15B52) Applications of hypergeometric functions (33C90)

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Some recent methods for establishing universality limits ⋮ Universality limits in the bulk for varying measures

Cites Work

• A note on the eigenvalue density of random matrices
• Bounds for orthogonal polynomials for exponential weights
• Contracted zero distributions of extremal polynomials associated with slowly decaying weights
• On the statistical mechanics approach in the random matrix theory: Integrated density of states.
• Asymptotics for orthogonal polynomials
• On fluctuations of eigenvalues of random Hermitian matrices.
• Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
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