Special function solutions of Painlevé equations: theory, asymptotics and applications
From MaRDI portal
Publication:2658252
DOI10.1007/978-3-030-56190-1_4zbMath1460.33023OpenAlexW3129504207MaRDI QIDQ2658252
Publication date: 19 March 2021
Full work available at URL: https://doi.org/10.1007/978-3-030-56190-1_4
orthogonal polynomialsrandom matricesPainlevé-type functionsasymptotic representations in the complex plane
Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Painlevé-type functions (33E17)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Hankel determinant and orthogonal polynomials for a Gaussian weight with a discontinuity at the edge
- The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation
- Asymptotics for products of characteristic polynomials in classical \(\beta\)-ensembles
- A computational exploration of the second Painlevé equation
- Numerical solution of Riemann-Hilbert problems: Painlevé II
- Painlevé V and a Pollaczek-Jacobi type orthogonal polynomials
- Hankel determinant approach to generalized Vorob'ev-Yablonski polynomials and their roots
- Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
- Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
- The isomonodromy approach to matrix models in 2D quantum gravity
- Determinants and their applications in mathematical physics
- Large \(z\) asymptotics for special function solutions of Painlevé II in the complex plane
- Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces
- Asymptotics for Hankel determinants associated to a Hermite weight with a varying discontinuity
- Painlevé IV critical asymptotics for orthogonal polynomials in the complex plane
- Painlevé differential equations in the complex plane
- 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.
- On the probability of positive-definiteness in the gGUE via semi-classical Laguerre polynomials
- Correlations of the characteristic polynomials in the Gaussian unitary ensemble or a singular Hankel determinant
- Multi-critical unitary random matrix ensembles and the general Painlevé II equation
- Asymptotics of the partition function of a random matrix model.
- Riemann–Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions
- A Generalized Freud Weight
- On Airy Solutions of the Second Painlevé Equation
- The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation
- Large-degree asymptotics of rational Painlevé-II functions: noncritical behaviour
- Asymptotic Methods for Integrals
- Zeros of Large Degree Vorob’ev–Yablonski Polynomials via a Hankel Determinant Identity
- Discrete Painlevé equations for recurrence coefficients of semiclassical Laguerre polynomials
- Painlevé VI and the Unitary Jacobi Ensembles
- On the numerical evaluation of Fredholm determinants
- Gaussian Unitary Ensemble with Boundary Spectrum Singularity and σ‐Form of the Painlevé II Equation
- Orthogonal Polynomials and Painlevé Equations
- Rational Solutions of the Painlevé‐III Equation
- Application of the τ‐function theory of Painlevé equations to random matrices: PV, PIII, the LUE, JUE, and CUE
- Large-Degree Asymptotics of Rational Painlevé-IV Functions Associated to Generalized Hermite Polynomials
- Large-degree asymptotics of rational Painlevé-II functions: critical behaviour
- Painlevé V and time-dependent Jacobi polynomials
- Application of the \(\tau\)-function theory of Painlevé equations to random matrices: PIV, PII and the GUE.
