Relationships between τ-functions and Fredholm determinant expressions for gap probabilities in random matrix theory

DOI10.1088/0951-7715/19/7/012zbMath1116.15020arXivmath-ph/0604027OpenAlexW2070147787MaRDI QIDQ3423058

Patrick Desrosiers, Peter J. Forrester

Publication date: 20 February 2007

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0604027

zbMATH Keywords

Gaussian unitary ensembleGaussian symplectic ensembleeigenvalue densityGaussian orthogonal ensemblerandom matrix ensemblehard edge scalingsoft edge scaling

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Probabilistic measure theory (60A10) Random matrices (algebraic aspects) (15B52) Fredholm integral equations (45B05)

Related Items (5)

A Riemann-Hilbert approach to Fredholm determinants of Hankel composition operators: scalar-valued kernels ⋮ Finite size corrections relating to distributions of the length of longest increasing subsequences ⋮ Asymptotic expansions relating to the distribution of the length of longest increasing subsequences ⋮ Edge distribution of thinned real eigenvalues in the real Ginibre ensemble ⋮ Multi-state asymmetric simple exclusion processes

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