Application of theτ-function theory of Painlevé equations to random matrices:PVI, the JUE, CyUE, cJUE and scaled limits

DOI10.1017/S0027763000008801zbMath1056.15023arXivmath-ph/0204008OpenAlexW2117755838MaRDI QIDQ4818204

Peter J. Forrester, Nicholas S. Witte

Publication date: 27 September 2004

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0204008

zbMATH Keywords

eigenvalueHamiltonianpercolationIsing modelrandom matrixPainlevé equationscircular unitary ensembleJacobi unitary ensembleLaguerre orthogonal ensembleCauchy unitary ensembleOkamoto \(\tau\)-function

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Eigenvalues, singular values, and eigenvectors (15A18) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Explicit solutions, first integrals of ordinary differential equations (34A05) Percolation (82B43) Random matrices (algebraic aspects) (15B52) Painlevé-type functions (33E17)

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