Chapter
3.5 Correlated Wishart matrices
3.6 Jacobi ensemble and Wishart matrices
3.7 Jacobi ensemble and symmetric spaces
3.8 Jacobi ensemble and quantum conductance
3.9 A circular Jacobi ensemble
3.12 Circular Jacobi β-ensemble
Chapter 4. The Selberg integral
4.2 Anderson's derivation
4.3 Consequences for the β-ensembles
4.4 Generalization of the Dixon-Anderson integral
4.5 Dotsenko and Fateev's derivation
4.7 Normalization of the eigenvalue p.d.f.'s
Chapter 5. Correlation functions at β = 2
5.1 Successive integrations
5.2 Functional differentiation and integral equation approaches
5.3 Ratios of characteristic polynomials
5.4 The classical weights
5.5 Circular ensembles and the classical groups
5.6 Log-gas systems with periodic boundary conditions
5.7 Partition function in the case of a general potential
5.8 Biorthogonal structures
5.9 Determinantal k-component systems
Chapter 6. Correlation functions at β = 1 and 4
6.1 Correlation functions at β = 4
6.2 Construction of the skew orthogonal polynomials at β = 4
6.3 Correlation functions at β = 1
6.4 Construction of the skew orthogonal polynomials and summation formulas
6.5 Alternate correlations at β = 1
6.6 Superimposed β = 1 systems
6.7 A two-component log-gas with charge ratio 1:2
Chapter 7. Scaled limits at β = 1, 2 and 4
7.1 Scaled limits at β = 2 — Gaussian ensembles
7.2 Scaled limits at β = 2 — Laguerre and Jacobi ensembles
7.3 Log-gas systems with periodic boundary conditions
7.4 Asymptotic behavior of the one- and two-point functions at β = 2
7.5 Bulk scaling and the zeros of the Riemann zeta function
7.6 Scaled limits at β = 4 — Gaussian ensemble
7.7 Scaled limits at β = 4 — Laguerre and Jacobi ensembles
7.8 Scaled limits at β = 1 — Gaussian ensemble
7.9 Scaled limits at β = 1 — Laguerre and Jacobi ensembles
7.10 Two-component log-gas with charge ratio 1:2
Chapter 8. Eigenvalue probabilities — Painlevé systems approach
8.2 Hamiltonian formulation of the Painlevé theory
8.3 σ-form Painlevé equation characterizations
8.4 The cases β = 1 and 4 — circular ensembles and bulk
8.5 Discrete Painlevé equations
8.6 Orthogonal polynomial approach
Chapter 9. Eigenvalue probabilities — Fredholm determinant approach
9.1 Fredholm determinants
9.2 Numerical computations using Fredholm determinants
9.6 Eigenvalue expansions for gap probabilities
9.7 The probabilities E[sub(β)][sup(soft)] (n; (s, ∞)) for β = 1, 4
9.8 The probabilities E[sub(β)][sup(hard)] ( n; (0, s); a) for β = 1, 4
9.9 Riemann-Hilbert viewpoint
9.10 Nonlinear equations from the Virasoro constraints
Chapter 10. Lattice paths and growth models
10.1 Counting formulas for directed nonintersecting paths
10.3 Discrete polynuclear growth model
10.4 Further interpretations and variants of the RSK correspondence
10.5 Symmetrized growth models
10.6 The Hammersley process
10.7 Symmetrized permutation matrices
10.8 Gap probabilities and scaled limits
10.9 Hammersley process with sources on the boundary
Chapter 11. The Calogero–Sutherland model
11.1 Shifted mean parameter-dependent Gaussian random matrices
11.2 Other parameter-dependent ensembles
11.3 The Calogero-Sutherland quantum systems
11.4 The Schrödinger operators with exchange terms
11.5 The operators H[sup((H, Ex))], H[sup((L, Ex))] and H[sup((J, Ex))]
11.6 Dynamical correlations for β = 2
Chapter 12. Jack polynomials
12.1 Nonsymmetric Jack polynomials
12.2 Recurrence relations
12.3 Application of the recurrences
12.4 A generalized binomial theorem and an integration formula
12.5 Interpolation nonsymmetric Jack polynomials
12.6 The symmetric Jack polynomials
12.7 Interpolation symmetric Jack polynomials
Chapter 13. Correlations for general β
13.1 Hypergeometric functions and Selberg correlation integrals
13.2 Correlations at even β
13.3 Generalized classical polynomials
13.4 Green functions and zonal polynomials
13.5 Inter-relations for spacing distributions
13.6 Stochastic differential equations
13.7 Dynamical correlations in the circular β ensemble
Chapter 14. Fluctuation formulas and universal behavior of correlations
14.2 Macroscopic balance and density
14.3 Variance of a linear statistic
14.4 Gaussian fluctuations of a linear statistic
14.5 Charge and potential fluctuations
14.6 Asymptotic properties of E[sub(β)](n; J) and P[sub(β)](n; J)
14.7 Dynamical correlations
Chapter 15. The two-dimensional one-component plasma
15.1 Complex random matrices and polynomials
15.2 Quantum particles in a magnetic field
15.3 Correlation functions
15.4 General properties of the correlations and fluctuation formulas
15.5 Spacing distributions
15.8 Metallic boundary conditions
15.9 Antimetallic boundary conditions
15.10 Eigenvalues of real random matrices
15.11 Classification of non-Hermitian random matrices
Log-Gases and Random Matrices (LMS-34)
：Log-Gases and Random Matrices (LMS-34)
( London Mathematical Society Monographs )
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